Displaying similar documents to “Zero product preservers and orthogonality preservers on algebras of unbounded operators.”

Hyperidentities in many-sorted algebras

Klaus Denecke, Somsak Lekkoksung (2009)

Discussiones Mathematicae - General Algebra and Applications

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The theory of hyperidentities generalizes the equational theory of universal algebras and is applicable in several fields of science, especially in computers sciences (see e.g. [2,1]). The main tool to study hyperidentities is the concept of a hypersubstitution. Hypersubstitutions of many-sorted algebras were studied in [3]. On the basis of hypersubstitutions one defines a pair of closure operators which turns out to be a conjugate pair. The theory of conjugate pairs of additive closure...

How to solve an operator equation.

Martin Mathieu (1992)

Publicacions Matemàtiques

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This article summarizes a series of lectures delivered at the Mathematics Department of the University of Leipzig, Germany, in April 1991, which were to overview techniques for solving operator equations on C*-algebras connected with methods developed in a Spanish-German research project on "Structure and Applications of C*-Algebras of Quotients" (SACQ). One of the researchers in this project was Professor Pere Menal until his unexpected death this April. To his memory this paper shall...

Algebras of quotients with bounded evaluation of a normed semiprime algebra

M. Cabrera, Amir A. Mohammed (2003)

Studia Mathematica

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We deal with the algebras consisting of the quotients that produce bounded evaluation on suitable ideals of the multiplication algebra of a normed semiprime algebra A. These algebras of quotients, which contain A, are subalgebras of the bounded algebras of quotients of A, and they have an algebra seminorm for which the relevant inclusions are continuous. We compute these algebras of quotients for some norm ideals on a Hilbert space H: 1) the algebras of quotients with bounded evaluation...

Compactness conditions for elementary operators

Matej Brešar, Yuri V. Turovskii (2007)

Studia Mathematica

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Various topics concerning compact elementary operators on Banach algebras are studied: their ranges, their coefficients, and the structure of algebras having nontrivial compact elementary operators. In the first part of the paper we consider separately elementary operators of certain simple types. In the second part we obtain our main results which deal with general elementary operators.

Mappings preserving zero products

M. A. Chebotar, W.-F. Ke, P.-H. Lee, N.-C. Wong (2003)

Studia Mathematica

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Let θ : ℳ → 𝓝 be a zero-product preserving linear map between algebras. We show that under some mild conditions θ is a product of a central element and an algebra homomorphism. Our result applies to matrix algebras, standard operator algebras, C*-algebras and W*-algebras.

Nonassociative real H*-algebras.

Miguel Cabrera, José Martínez Aroza, Angel Rodríguez Palacios (1988)

Publicacions Matemàtiques

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We prove that, if A denotes a topologically simple real (non-associative) H*-algebra, then either A is a topologically simple complex H*-algebra regarded as real H*-algebra or there is a topologically simple complex H*-algebra B with *-involution τ such that A = {b ∈ B : τ(b) = b*}. Using this, we obtain our main result, namely: (algebraically) isomorphic topologically simple real H*-algebras are actually *-isometrically isomorphic.

On local derivations in the Kadison sense

Andrzej Nowicki (2001)

Colloquium Mathematicae

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Let k be a field. We prove that any polynomial ring over k is a Kadison algebra if and only if k is infinite. Moreover, we present some new examples of Kadison algebras and examples of algebras which are not Kadison algebras.