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Schur and operator multipliers

Ivan G. Todorov, Lyudmila Turowska (2010)

Banach Center Publications

The present article is a survey of known results on Schur and operator multipliers. It starts with the classical description of Schur multipliers due to Grothendieck, followed by a discussion of measurable Schur multipliers and a generalisation of Grothendieck's Theorem due to Peller. Thereafter, a non-commutative version of Schur multipliers, called operator multipliers and introduced by Kissin and Schulman, is discussed, and a characterisation extending the description in the commutative case...

Sequentially Right Banach spaces of order p

Mahdi Dehghani, Mohammad B. Dehghani, Mohammad S. Moshtaghioun (2020)

Commentationes Mathematicae Universitatis Carolinae

We introduce and study two new classes of Banach spaces, the so-called sequentially Right Banach spaces of order p , and those defined by the dual property, the sequentially Right * Banach spaces of order p for 1 p . These classes of Banach spaces are characterized by the notions of L p -limited sets in the corresponding dual space and R p * subsets of the involved Banach space, respectively. In particular, we investigate whether the injective tensor product of a Banach space X and a reflexive Banach space...

Sets of p-multiplicity in locally compact groups

I. G. Todorov, L. Turowska (2015)

Studia Mathematica

We initiate the study of sets of p-multiplicity in locally compact groups and their operator versions. We show that a closed subset E of a second countable locally compact group G is a set of p-multiplicity if and only if E * = ( s , t ) : t s - 1 E is a set of operator p-multiplicity. We exhibit examples of sets of p-multiplicity, establish preservation properties for unions and direct products, and prove a p-version of the Stone-von Neumann Theorem.

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