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Spectral Synthesis and Operator Synthesis for Compact Groups
Author(s) -
Spronk Nico,
Turowska Lyudmila
Publication year - 2002
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610702003356
Subject(s) - tensor product , mathematics , algebra over a field , pure mathematics , operator (biology) , operator algebra , haar measure , diagonal , measure (data warehouse) , crossed product , group algebra , group (periodic table) , product (mathematics) , computer science , biochemistry , chemistry , geometry , organic chemistry , repressor , database , transcription factor , gene
Let G be a compact group and C( G ) be the C * ‐algebra of continuous complex‐valued functions on G . The paper constructs an imbedding of the Fourier algebra A( G ) of G into the algebra V( G ) = C( G )⊗ h C( G ) (Haagerup tensor product) and deduces results about parallel spectral synthesis, generalizing a result of Varopoulos. It then characterizes which diagonal sets in G × G are sets of operator synthesis with respect to the Haar measure, using the definition of operator synthesis due to Arveson. This result is applied to obtain an analogue of a result of Froelich: a tensor formula for the algebras associated with the pre‐orders defined by closed unital subsemigroups of G .