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Shulman, V., Todorov, I. och Turowska, L. (2015) *Sets of multiplicity and closable multipliers on group algebras*.

** BibTeX **

@article{

Shulman2015,

author={Shulman, Victor and Todorov, Ivan G. and Turowska, Lyudmila},

title={Sets of multiplicity and closable multipliers on group algebras},

journal={Journal of Functional Analysis},

issn={0022-1236},

volume={268},

issue={6},

pages={1454-1508},

abstract={We undertake a detailed study of the sets of multiplicity in a second countable locally compact group G and their operator versions. We establish a symbolic calculus for normal completely bounded maps from the space B(L2(G)) of bounded linear operators on L2(G) into the von Neumann algebra VN(G) of G and use it to show that a closed subset E⊆G is a set of multiplicity if and only if the set E⁎={(s,t)∈G×G:ts−1∈E} is a set of operator multiplicity. Analogous results are established for M1-sets and M0-sets. We show that the property of being a set of multiplicity is preserved under various operations, including taking direct products, and establish an Inverse Image Theorem for such sets. We characterise the sets of finite width that are also sets of operator multiplicity, and show that every compact operator supported on a set of finite width can be approximated by sums of rank one operators supported on the same set. We show that, if G satisfies a mild approximation condition, pointwise multiplication by a given measurable function ψ:G→C defines a closable multiplier on the reduced C⁎-algebra View the MathML source of G if and only if Schur multiplication by the function N(ψ):G×G→C, given by N(ψ)(s,t)=ψ(ts−1), is a closable operator when viewed as a densely defined linear map on the space of compact operators on L2(G). Similar results are obtained for multipliers on VN(G).},

year={2015},

keywords={Sets of multiplicity; Masa; Bimodule; Schur multiplier},

}

** RefWorks **

RT Journal Article

SR Electronic

ID 227345

A1 Shulman, Victor

A1 Todorov, Ivan G.

A1 Turowska, Lyudmila

T1 Sets of multiplicity and closable multipliers on group algebras

YR 2015

JF Journal of Functional Analysis

SN 0022-1236

VO 268

IS 6

SP 1454

OP 1508

AB We undertake a detailed study of the sets of multiplicity in a second countable locally compact group G and their operator versions. We establish a symbolic calculus for normal completely bounded maps from the space B(L2(G)) of bounded linear operators on L2(G) into the von Neumann algebra VN(G) of G and use it to show that a closed subset E⊆G is a set of multiplicity if and only if the set E⁎={(s,t)∈G×G:ts−1∈E} is a set of operator multiplicity. Analogous results are established for M1-sets and M0-sets. We show that the property of being a set of multiplicity is preserved under various operations, including taking direct products, and establish an Inverse Image Theorem for such sets. We characterise the sets of finite width that are also sets of operator multiplicity, and show that every compact operator supported on a set of finite width can be approximated by sums of rank one operators supported on the same set. We show that, if G satisfies a mild approximation condition, pointwise multiplication by a given measurable function ψ:G→C defines a closable multiplier on the reduced C⁎-algebra View the MathML source of G if and only if Schur multiplication by the function N(ψ):G×G→C, given by N(ψ)(s,t)=ψ(ts−1), is a closable operator when viewed as a densely defined linear map on the space of compact operators on L2(G). Similar results are obtained for multipliers on VN(G).

LA eng

DO 10.1016/j.jfa.2014.11.019

LK http://dx.doi.org/10.1016/j.jfa.2014.11.019

OL 30