Professor Edward Kissin has a PhD in Pure Mathematics and a BSc (First Class) in Mathematics and Physics. He is a Professor of Pure Mathematics in the School of Computing and Digital Media.

## Professor Edward Kissin

Professor Edward Kissin is a Professor of Mathematics, STORM. He has a BSc (First Class) in Mathematics and Physics and PhD in Pure Mathematics from Moscow Institute of Physics and Technology.

From 1970 till 1981 he worked in Moscow Institute of Radio Engineering as a Lecturer, a Senior Lecturer and an Associate Professor in the Department of Mathematics. In 1982 he moved to Britain and became a Research Fellow in the Mathematics Department and a part-time Lecturer in the Economics Department at the University of Birmingham.

In 1984 he became a Mathematics lecturer at London Metropolitan University. Since then he has been Senior Lecturer and in 1993 he became a Professor of Pure Mathematics.

He presents in numerous mathematical conferences and gives talks in many other national universities, as well as abroad. He's previously had grants from the London Mathematical Society, EPSRC and the Leverhulme Trust (Research Leave Grant).

### Professional affiliation

- Member of the London Mathematical Society

Dr Edward Kissin has the following areas of expertise:

- Functional Analysis
- C*-algebras
- W*-algebras
- Banach *-algebras
- Representations on Krein spaces
- Reflexive algebras of operators
- Representations of Lie groups
- Lie algebras of operators
- Operator smooth functions

He also teaches the following modules:

- Linear Algebra
- Real Variable Analysis
- Complex Variable Analysis

**Books**

1. (with V. Shulman) "Representations on Krein Spaces and Derivations of C*-algebras", Addison Wesley Longman, 1997, 602 pp.

**Papers**

1. Decomposition of a tensor product of irreducible maximally degenerate representations of the group of n-th order complex matrices with determinant 1, Soviet Mathematics (Doklady Akademii Nauk SSSR) 11(1970), 183-87.

2. Decomposition of the tensor product of some representations of the group SL(n,C) into irreducible representations, Uspkhi Matematicheskikh Nauk, 26(1971), 225-26.

3. Decomposition of the restriction of the representation of the group SL(n,C) to the subgroup SL(3,C) into irreducible representations, Trudy Moskovskogo Instituta Radiotekhniki, Elektroniki i Avtomatiki, 52(1971), 37-46.

4. Decomposition of tensor products of some representations of the complex unimodular group of n-th order matrices into irreducible representations, Thesis abstract, Moscow (1971).

5. Decomposition of the tensor product of representations of the group SL(n,C) into irreducible components, Uspekhi Matematicheskikh Nauk, 27(1972).

6. Decomposition of tensor products of representations in the principal series with repre-sentations in the supplementary series of the group SL(n,C) into irreducible components, Trudy Moskovskogo Inst. Radiotekhniki, Elektroniki i Avtomatiki, 67(1973), 65-78.

7. Decomposition of certain tensor products of representations in the principal series with representations in the supplementary series of the group SL(n,C) into irreducible components, Funkzionalnii Analiz i ego prilozeniya, 8(1974), 166-68.

8. C*-algebras generated by dynamical systems and weighted shifts, Soviet Mathematics (Doklady Akademii Nauk SSSR), 15(1974), 957-61.

9. C*-algebras generated by dynamical systems and N-dimensional weighted shifts, Soviet Mathematics (Dokl. Akad. Nauk SSSR), 15(1974), 1733-37.

10. Irreducible representations of some C*-algebras, Information Archive of the All-Union Inst. of Scientific and Technical Information, 1977

11. On some reflexive algebras of operators and the operator Lie algebras of their derivations, Proceedings of the London Mathematical Society, (3), 49(1984), 1-35.

12. On normed Lie algebras with sufficiently many subalgebras of codimension 1, Proceedings of the Edinburgh Mathematical Society, 29(1986), 1-22.

13. On some reflexive operator algebras constructed from two sets of closed operators and from a set of reflexive operator algebras, Pacific Journal of Mathematics, 126(1987), 125-143.

14. On lattices of invariant subspaces of operator algebras, Journal of Operator Theory, 18(1987), 373-392.

15. Invariant subspaces for derivations, Proceedings of the American Mathematical Society, 102(1988), 95-101.

16. Totally symmetric algebras and the similarity problem, Journal of Functional Analysis, 77(1988), 88-97.

17. Symmetric operator extensions of unbounded derivations of C*-algebras, Journal of Functional Analysis, 81(1988), 38-53.

18. On derivations of operator algebras implemented by bounded operators, Proceedings of Symposia in Pure Mathematics, 51(1990), Part 2, 163-174.

19. On some reflexive lattices of subspaces, Journal of Operator Theory, 25(1991) 141-162.

20. Dissipative implementations of *-derivations of C*-algebras and representations in indefinite metric spaces, Journal of the London Mathematical Society, 43(1991), 451-64.

21. Deficiency-indices sets of unbounded derivations of C*-algebras, Proceedings of OATE II, Longman, 1992, 128-139.

22. Indices of unbounded derivations of C*-algebras, Pacific Journal of Mathematics, 152(1992), 125-50.

23. Representational indices of derivations of C*-algebras and repre- sentations of *-algebras on indefinite metric spaces, Journal fur die reine und angew. Math., 439(1992), 72-93.

24. (with V. Shulman) Dense Q-subalgebras of Banach and C*-algebras and unbounded derivations of Banach and C*-algebras, Proceedings of Edinburgh Mathematical Society, 36(1993), 261-276.

25. On the Uniqueness of Representational Indices of Derivations of C*-algebras, Pacific Journal of Mathematics, 162(1994), 97-120.

26. Superderivation of C*-algebras, Communications in Mathematical Physics, 160(1994), 333-348.

27. (with V. Shulman) Differential Properties of Some Dense Subalgebras of Banach and C*-algebras, Proceedings of Edinburgh Mathematical Society, 37(1994), 399-422.

28. Semigroups of Representational Indices of Derivations of C*-algebras, Journal of Functional Analysis, 126(1994), 139-168.

29. Derivations of the algebra C(H) of all compact operators and representations of Q-subalgebras of C(H) on k-spaces, Journal of the London Mathematical Society, 51(1995), 161-174.

30. (with A. Loginov and V. Shulman) Derivations of C*-algebras and almost Hermitian representations on k-spaces, Pacific Journal of Mathematics, 174(1996), 411-430.

31. (with V. Shulman) Operator differentiable functions and derivations of operator algebras, Funktsionalnii Analiz i ego priloziniya, 4, 30(1996), 75-77.

32. Derivations of C*-algebras and representations on deficiency spaces of skew-symmetric operators, Proceedings of the London Mathematical Society, 76(1998), 476-496.

33. (with V. Shulman) Differential Banach *-algebras of compact operators associated with symmetric operators, Journal of Functional Analysis, 156(1998), 1-29.

34. (with V. Shulman) Dual Spaces and Isomorphisms of some Differential Banach *-Algebras of Operators, Pacific Journal of Mathematics, 190(1999), 329-360.

35. (with V. Shulman) Differential Schatten *-algebras. Approximation property and approximate identities, Journal of Operator Theory, 45(2001), 303-334.

36. (with V. Shulman) On the range inclusion of normal derivations: variations on a theme by Johnson, Williams and Fong, Proceedings of the London Mathematical Society, 83(2001), 176-198.

37. (with V. Shulman) Some Classes of Positive Functionals on Banach *-algebras, Proceedings of the Conference on Modeling and Optimization, Vologda, 2001, 221-223.

38. (with V. Shulman) On a Problem of J. P. Williams, Proceedings of the American Mathematical Society, 130(2002), 3605-3608.

39. (with V. Shulman) Range-inclusive maps from subspaces of C*-algebras, Quart. Journal Math. Oxford, 53(2002), 455-465.

40. Stability of the Deficiency Indices of Symmetric Operators under Selfadjoint Perturbations, Proceedings of Edinburgh Mathematical Society, 46(2003), No 2, 383-394.

41. (with V.Lomonosov and V. Shulman) Implementation of Derivations and Invariant Subspaces, Israel Journal of Mathematics, 134(2003), 1-28.

42. (with V. Shulman) Schur Multipliers, -Topology and C*-algebras, Proceedings of the Conference on Modeling and Optimization, Vologda, 2003, 145-148.

43. (with V. Shulman) Classes of Operator-Smooth Functions. II. Operator Differentiable Functions, Integral Equations and Operator Theory, 49(2004), No 2, 165-210.

44. (with V. Shulman) Classes of Operator-Smooth Functions. I. Operator Lipschitz functions, Proceedings of Edinburgh Mathematical Soc. 48(2005), 151-173.

45. (with V. Shulman) Classes of Operator-Smooth Functions. II. Operator Stable functions

and Fuglede ideals, Proceedings of Edinburgh Mathematical Soc., 48(2005), 175-197.

46. Reflexive *-derivations and lattices of invariant spaces of operator algebras associated

with them, Journal of Functional Analysis, 232(2006), 56-89

47. (with V. Shulman) Lipschitz functions on Hermitian Banach *-algebras, Quarterly

Journal of Mathematics Oxford, 57(2)(2006), 215-239.

48. (with V. Shulman) Operator Multipliers, Pacific Journal of Mathematics, 227(1)(2006), 109-142.

49. (with V. Shulman and L. Turowska) Extension of Operator Lipschitz and Commutator Bounded functions, Operator Theory: Advances and Applications, 171(2006), 225-244.

50. On action of diffeomorphisms of C*-algebras on derivations, Journal of Functional Analysis, 236(2006), 609-629.

51. (with V. Shulman) Functions acting on symmetrically normed ideals and on the domains of derivations on these ideals, Journal of Operator Theory, 58:1(2007), 63-82.

52. On Clarkson-McCarthy inequalities for n-tuples of operators, Proceedings of Amer. Math. Society, Proc. AMS 135(2007), 2483-2495.

53. (with V. Shulman) On fully operator Lipschitz functions, Journal of Functional Analysis, 253(2)(2007), 711-728.

54. (with M. Bresar and V. Shulman) On Jordan ideals and submodules: algebraic and analytic aspects, Funk. Anal. and its Applications, 42:3(2008), 71-75.

55. (with M. Bresar and V. Shulman) When Jordan submodules are bimodules, Quarterly

Journal of Mathematics Oxford, 59(4) (2008), 409-440, doi:10.1093/qmath/ham053

56. (with M. Bresar and V. Shulman) Lie ideals: from pure algebra to C*-algebras, Journal fur die reine und angew. Math. (Crelle), 623(2008), 73-121.

57. (with V. Shulman and Yu. Turovskii), Banach Lie algebras with Lie subalgebras of finite codimension: their invariant subspaces and Lie ideals, Journal of Functional Analysis, 256 (2009), 323-351, doi: 10.1016/j.jfa.2008.10.012.

58. (with V. Shulman and Yu. Turovskii), Banach Lie algebras with Lie subalgebras of finite codimension have Lie ideals, Journal of London Mathematical Society, (2) 80(2009), 603-626, doi: 10.1112/jlms/jdp046.

59. (with D.S. Potapov, V.S. Shulman and F.A. Sukochev), Lipschitz Functions, Schatten Ideals and Unbounded Derivations, Journal of Functional Analysis and its Applications, 45, No. 2, (2011), 93-96, DOI: 10.1007/s10688-011-0018-5

60. (with D.S. Potapov, V.S. Shulman and F.A. Sukochev), Operator smoothness in Schatten norms for functions of several variables: Lipschitz conditions, differentiability and unbounded derivations, Proceedings of the London Mathematical Society, 105(2012), 661-702, doi:10.1112/plms/pds014.

61. (with V. Shulman and Yu. Turovskii) Topological radicals and Frattini theory of Banach Lie algebras, Journal of Integral Equations and Operator Theory, No 1, 74(2012), 51-121, doi:10.1007/s00020-012-1990-8

62. (with T. Formisano) Minimax conditions for Schatten ideals of compact operators, Eurasian Mathematical Journal, 3(1), (2012), 29-40.

63. (with V. Lomonosov and Yu. Turovskii) Victor Shulman: The Gentle Art of Mathematics, Operator Theory: Advances and Applications, Algebraic Methods in Functional Analysis, 233(2013), 1-16. Doi 10.1007/978-3-0348-0502-5.

64. (with T. Formisano) Clarkson-McCarthy inequalities for l¬¬p-spaces of operators in Schatten ideals, Journal of Integral Equations and Operator Theory, 79(2) (2014), 151-173. DOI: 10.1007/s00020-014-2145-x.

65. (with V.S. Shulman) On 1-cohomologies of nilpotent groups, Proceedings of the Volog. State Univ. (2014), 35-39 .

66. (with V.S. Shulman) Representations of nilpotent groups: extensions, neutral cohomology, Pontryagin spaces, Journal of Functional Analysis and its Applications, 49(3) (2015), 222-225.

67. (with V.S. Shulman) Non-unitary representations of nilpotent groups, I: cohomologies, extensions and neutral cocycles, Journal of Functional Analysis, 269(2015), 2564-2610. DOI: 10.1016/j.jfa.2015.07.003

68. (with V.S. Shulman) Representations of nilpotent groups on spaces with indefinite metric, Journal of Integral Equations and Operator Theory, 87, No 1(2017), 81-116, DOI 10.1007/s00020-016-2337-7.

69. (with V. Shulman and Yu. Turovski) On theory of topological radicals, Contemporary Mathematics, Fundamental directions (Journal of Mathematical Sciences) 64, No 3 (2018), 490-546.

70. (with V. Shulman and Yu. Turovski) Relations and radicals in abstract lattices and in lattices of subspaces of Banach spaces and ideals of Banach algebras. Amitsur’s theory revisited. arXiv: 1903.12291 [math FA], DOI: 10.13140/RG.2.2.15979.59687.

71. Relations and trails in lattices of projections in W*-algebras, Proceedings of the Edinburgh Mathematical Society, 62(2019), 1189-1215.

72. (with V. Shulman) Cohomology of groups with normal Engel subgroups, Proceedings of 10 International Science and Technology Conference, Vologda, 2019 (ISBN 978-5-87851-872-7) (INFOS-2019), 4-8. DOI.10.131140/RG.2.2.25937.38243

73. (with V. Shulman and Yu. Turovski) Pontryagin-Krein Theorem: Lomonosov’s proof and related results, to appear.

74. (with V. Shulman and Yu. Turovski) From Lomonosov Lemma to radical approach in joint spectral radius theory, to appear.

** **e.kissin@londonmet.ac.uk

+44 (0)20 7133 4633