Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
The purpose of this paper is to give an illustration of how operator theoretic results in Hilbert space can be applied to obtain results in classical and abstract harmonic analysis. An inequality for integral operators will be used to... more
The purpose of this paper is to give an illustration of how operator theoretic results in Hilbert space can be applied to obtain results in classical and abstract harmonic analysis. An inequality for integral operators will be used to give new proofs for the classical Hausdorff-...
Research Interests:
Abstract: A survey of known results and open problems concerning boundedness, compactness, and trace ideal membership of composition operators over the Bergman and Hardy spaces in several complex variables, with special attention to... more
Abstract: A survey of known results and open problems concerning boundedness, compactness, and trace ideal membership of composition operators over the Bergman and Hardy spaces in several complex variables, with special attention to strongly ...
Research Interests:
Research Interests:
Research Interests:
This paper is an elaborated version of the material presented by the author in a three hour minicourse at "V International Course of Mathematical Analysis in Andalusia," Almeria, Spain, September 12-16, 2011. Part I is devoted... more
This paper is an elaborated version of the material presented by the author in a three hour minicourse at "V International Course of Mathematical Analysis in Andalusia," Almeria, Spain, September 12-16, 2011. Part I is devoted to an exposition of the properties of derivations on various algebras and triple systems in finite and infinite dimensions, the primary questions addressed being whether the derivation is automatically continuous and to what extent it is an inner derivation. One section in Part I is devoted to the subject of contractive projections, which play an important role in the structure theory of Jordan triples and in Part III. Part II discusses cohomology theory of algebras and triple systems, in both finite and infinite dimensions. Although the cohomology of associative and Lie algebras is substantially developed, in both finite and infinite dimensions, the same could not be said for Jordan algebras. Moreover, the cohomology of triple systems has a rather s...
Abstract. A survey of known results and open problems concerning boundedness, compactness, and trace ideal membership of the small Hankel operator. The setting is either the Bergman or Hardy space over a bounded symmetric domain or a... more
Abstract. A survey of known results and open problems concerning boundedness, compactness, and trace ideal membership of the small Hankel operator. The setting is either the Bergman or Hardy space over a bounded symmetric domain or a strongly ...
Research Interests:
Research Interests:
An atomic decomposition is proved for Banach spaces which satisfy some affine geometric axioms compatible with notions from the quantum mechanical measuring process. This is then applied to yield, under appropriate assumptions, geometric... more
An atomic decomposition is proved for Banach spaces which satisfy some affine geometric axioms compatible with notions from the quantum mechanical measuring process. This is then applied to yield, under appropriate assumptions, geometric characterizations, up to isometry, of the unit ball of the dual space of a JB*-triple, and up to complete isometry, of one-sided ideals in C*-algebras.
Research Interests:
Given a JBW*-triple Z and a normal contractive projection P on Z, we show that the (Murray-von Neumann) type of each summand of P(Z) is dominated by the type of Z.
Research Interests:
We give a geometric realization of space-time spinors and associated representations, using the Jordan triple structure associated with the Cartan factors of type 4, the so-called spin factors. We construct certain representations of the... more
We give a geometric realization of space-time spinors and associated representations, using the Jordan triple structure associated with the Cartan factors of type 4, the so-called spin factors. We construct certain representations of the Lorentz group, ...
Research Interests:
Research Interests:
YAAKOV FRIEDMAN and BERNARD RUSSO/5*-triples (which will be defined later) occur in the study of bounded symmetric domains in finite and infinite dimensions. Каир [21] showed the equivalence of the two categories: bounded symmetric... more
YAAKOV FRIEDMAN and BERNARD RUSSO/5*-triples (which will be defined later) occur in the study of bounded symmetric domains in finite and infinite dimensions. Каир [21] showed the equivalence of the two categories: bounded symmetric domains in complex Banach ...
We discuss sharpness in the Hausdorff Young theorem for unimodular groups. First the functions on unimodular locally compact groups for which equality holds in the Hausdorff Young theorem are determined. Then it is shown that the... more
We discuss sharpness in the Hausdorff Young theorem for unimodular groups. First the functions on unimodular locally compact groups for which equality holds in the Hausdorff Young theorem are determined. Then it is shown that the Hausdorff Young theorem is not ...
Research Interests:
Abstract. We show that the range of a norm one projection on a commutative C*-algebra has a ternary product structure (Theorem 2). We describe and characterize all such projections in terms of extreme points in the unit ball of the image... more
Abstract. We show that the range of a norm one projection on a commutative C*-algebra has a ternary product structure (Theorem 2). We describe and characterize all such projections in terms of extreme points in the unit ball of the image of the dual (Theorem 1). We give ...
Research Interests:
Research Interests:
Research Interests:
Research Interests:
IN this paper we discuss the problem of characterizing geometrically those Banach spaces which admit an algebraic structure. For ordered Banach spaces well known results of Alfsen-Schultz [3] and Alfsen-Schultz-Hanche-Olsen [1] give... more
IN this paper we discuss the problem of characterizing geometrically those Banach spaces which admit an algebraic structure. For ordered Banach spaces well known results of Alfsen-Schultz [3] and Alfsen-Schultz-Hanche-Olsen [1] give geometric characterizations of the ...
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Abstract The Dunford-Pettis property is shown to hold for the uniform algebra A (Ω) and its dual for some standard domains Ω, including strongly pseudoconvex bounded domains in C n, pseudoconvex bounded domains of finite type in C 2, and... more
Abstract The Dunford-Pettis property is shown to hold for the uniform algebra A (Ω) and its dual for some standard domains Ω, including strongly pseudoconvex bounded domains in C n, pseudoconvex bounded domains of finite type in C 2, and bounded domains in C. ...
Research Interests:
Research Interests:
ABSTRACT A theorem of Hausdorff Young type is proved for integral operators in the setting of gage spaces. This theorem is used to show that the norm of the Lp-Fourier transform on unimodular groups is stable under compact extension.
Research Interests:
RefDoc Bienvenue - Welcome. Refdoc est un service / is powered by. ...
Research Interests:
ABSTRACT We introduce the notion of a Jordan triple module and determine the precise conditions under which every derivation from a JB * -triple E into a Banach (Jordan) triple E-module is continuous. In particular, every derivation from... more
ABSTRACT We introduce the notion of a Jordan triple module and determine the precise conditions under which every derivation from a JB * -triple E into a Banach (Jordan) triple E-module is continuous. In particular, every derivation from a real or complex JB * -triple into its dual space is automatically continuous. Among the consequences, we prove that every triple derivation from a C * -algebra A to a Banach triple A-module is continuous. In particular, every Jordan derivation from A to a Banach A-bimodule is a derivation, a result which complements a classical theorem due to B.E. Johnson and solves a problem which has remained open for over ten years.
Research Interests:
Research Interests:
1. Introduction. In his survey article on linear transformations of matrix algebras, M. Marcus [4; 838-839] states that not much can be said about a linear transformation T on the full n X n matrix algebra M,,(F) over a field F if it is... more
1. Introduction. In his survey article on linear transformations of matrix algebras, M. Marcus [4; 838-839] states that not much can be said about a linear transformation T on the full n X n matrix algebra M,,(F) over a field F if it is assumedonly that EI (T (A)) El (A), for all A in Mn ( ...
Research Interests:
Research Interests:
We study holomorphic functions / in the unit ball for which the small Hankel operator hf belongs to the Dixmier class.
Research Interests:
The Arens extension of the triple product of an associative triple system is studied. Using a representation theorem for C*-ternary rings due to Zettl, it is shown that the second dual of a C*-ternary ring is itself a C*-ternary ring