Herz-Schur multipliers of dynamical systems

• We extend the notion of a Herz-Schur multiplier to the setting of non-commutative dynamical systems: given a C*-algebra A, a locally compact group G, and an action alpha of C on A, we define transformations on the reduced crossed product of A by alpha which, in the case A = C, reduce to the classical Herz-Schur multipliers. We introduce Schur A-multipliers, establish a characterisation that generalises the classical descriptions of Schur multipliers, and present a transference theorem in the new setting, identifying isometrically the Herz-Schur multipliers of the dynamical system (A,G,alpha) with the invariant part, of the Schur A-multipliers. We discuss special classes of Herz-Schur multipliers, in particular, those associated to a locally compact abelian group G and its canonical action on the C*-algebra C* (Gamma) of the dual group Gamma. (C) 2018 Published by Elsevier Inc.

Ämnesord

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

NATURVETENSKAP  -- Matematik -- Algebra och logik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Algebra and Logic (hsv//eng)

NATURVETENSKAP  -- Matematik -- Geometri (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Geometry (hsv//eng)

NATURVETENSKAP  -- Matematik -- Matematisk analys (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Mathematical Analysis (hsv//eng)

Nyckelord

Herz-Schur multiplier

Crossed product

von-neumann-algebras

fourier algebras

representations

operators

maps

Mathematics

Crossed product

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