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A Factorization Theorem for Multiplier Algebras of Reproducing Kernel Hilbert Spaces

  Published:2011-08-31
 Printed: Jun 2013
  • Bebe Prunaru,
    Institute of Mathematics ``Simion Stoilow'' of the Romanian Academy, RO-014700 Bucharest, Romania
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Abstract

Let $(X,\mathcal B,\mu)$ be a $\sigma$-finite measure space and let $H\subset L^2(X,\mu)$ be a separable reproducing kernel Hilbert space on $X$. We show that the multiplier algebra of $H$ has property $(A_1(1))$.
Keywords: reproducing kernel Hilbert space, Berezin transform, dual algebra reproducing kernel Hilbert space, Berezin transform, dual algebra
MSC Classifications: 46E22, 47B32, 47L45 show english descriptions Hilbert spaces with reproducing kernels (= [proper] functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) [See also 47B32]
Operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-Rovnyak, and other structured spaces) [See also 46E22]
Dual algebras; weakly closed singly generated operator algebras
46E22 - Hilbert spaces with reproducing kernels (= [proper] functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) [See also 47B32]
47B32 - Operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-Rovnyak, and other structured spaces) [See also 46E22]
47L45 - Dual algebras; weakly closed singly generated operator algebras
 

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