publication . Preprint . 2015

Frames and outer frames for Hilbert C^*-modules

Arambašić, Ljiljana; Bakić, Damir;
Open Access English
  • Published: 15 Jul 2015
Abstract
The goal of the present paper is to extend the theory of frames for countably generated Hilbert $C^*$-modules over arbitrary $C^*$-algebras. In investigating the non-unital case we introduce the concept of outer frame as a sequence in the multiplier module $M(X)$ that has the standard frame property when applied to elements of the ambient module $X$. Given a Hilbert $\A$-module $X$, we prove that there is a bijective correspondence of the set of all adjointable surjections from the generalized Hilbert space $\ell^2(\A)$ to $X$ and the set consisting of all both frames and outer frames for $X$. Building on a unified approach to frames and outer frames we then obt...
Subjects
free text keywords: Mathematics - Operator Algebras, Mathematics - Functional Analysis, Primary 46L08, Secondary 42C15
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