## Bernard Russo

Professor and Chair, Mathematics

School of Physical Sciences

School of Physical Sciences

Chair, Mathematics

School of Physical Sciences

School of Physical Sciences

PH.D., University of California, Los Angeles, 1965

University of California, Irvine

263 Multipurpose Science & Technology Building

Mail Code: 3875

Irvine, CA 92697

263 Multipurpose Science & Technology Building

Mail Code: 3875

Irvine, CA 92697

**Research Interests**

Functional analysis, operator theory, operator algebras, Jordan structures

**Appointments**

1978-present: Professor, Department of Mathematics, UC Irvine

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**Research Abstract**

Early research interests were in algebras of operators on Hilbert space (von Neumann algebras) and their applications to abstract harmonic analysis (group representation theory) and operator theory. After that, Jordan operator algebras and triples and the ir connections with several complex variables and quantum mechanics have been the focus of study. Current main interest is the theory of operator spaces, or "quantized functional analysis".eÂn

**Publications**

"State spaces of JB*-triples" (with Matthew Neal), Mathematische Annalen, to appear*

"An operator space characterization of C*-algebras and ternary rings" (with Matthew Neal), Pacific Journal of Mathematics 209 (2003) pp 339-364`

"Derivatives on real and complex JB*-triples" (with A. Martinez, A. Peralta, T. Ho), Journal of the London Mathematical Society, 64 (2001), pp 85-102.

"Contractive projections and operator spaces" (with Matthew Neal), Comptes Rendus Acad. Sci. Paris 331 (2000), pp 873-878 (announcement); Transactions of the American Mathematical Society 355 (2003) pp 2223-2262.

"A new approach to the spinors and some representations of the Lorentz group on them" (with Yaakov Friedman), Foundations of PHysics 31 (2001),

pp 1733-1766.

pp 1733-1766.

"The small Hankel operator in several complex variables". Complex Analysis and Related Topics, Vol.114 (2000) of the series Operator Theory. Advances and Applications, Birkhauser Verlag, pp 235-252.

"Hankel operators in the Dixmier class" (with S. Y. Li), C.R. Acad. Sci., Paris, 325, serie I, 1997, pp.21-26.

"Holomorphic Composition Operators in several complex variables," In: Studies on Composition Operators, Proceedings of the Rocky Mountain Mathematics Consortium, July 8-19,1996; editors F. Jafari, B. MacCluer, C. Cowen, A. Porter, Contemp. Math. 213 (1998), 191-212.

"Spectral domains in several complex variables," (with S. Fu), Rocky Mountain Mathematical Journal 27 (1997), pp 1095-1116.

"Schatten class composition operators on weighted Bergman spaces of bounded symmetric domains," (with S.Y. Li), Annali di matematica pura ed applicata, (IV) Vol. CLXXII (1997), pp. 379-394.

"Structure of JB*-triples". Jordan algebras, Proceedings of Oberwohlfach Conference (1992), deGruyter, Berlin, 1994, pp 209-280.

**Professional Societies**

Associate Secretary for the Western Section, American Mathematical Society 1998-2002

**Last updated**

08/11/2003