A module frame concept for Hilbert C*-modules

By M. Frank, D. Larson. 2000

95 citations recorded by the source corpus.

The goal of the present paper is a short introduction to a general module frame theory in C*-algebras and Hilbert C*-modules. The reported investigations rely on the idea of geometric dilation to standard Hilbert C*-modules over unital C*-algebras that possess orthonormal bases, and of reconstruction of the frames by projections and other bounded module operators with suitable ranges. We obtain frame representation and decomposition theorems, as well as similarity and equivalence results. The relative position of two and more frames in terms of being complementary or disjoint is investigated in detail. In the last section some recent results by P. G. Casazza are generalized to our setting. The Hilbert space situation appears as a special case. For detailled proofs we refer to another paper also contained in the ArXiv.

Subfields: Algebra and Number Theory, Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/ae8439e885ee759c423fcd2d161e92f03535f62b

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. S. Thompson
2. Iain Raeburn
3. D. Larson
4. Trent Yeend
5. Aidan Sims
6. M. Tomforde
7. Roozbeh Hazrat

In Applied Mathematics

1. V. Kaftal
2. Shuang Zhang
3. S. Thompson
4. Iain Raeburn
5. D. Larson

In Mathematical Physics

1. S. Thompson
2. Iain Raeburn
3. V. Kaftal
4. Shuang Zhang
5. D. Larson
6. Aidan Sims
7. Trent Yeend
8. M. Tomforde

Citations in the corpus

• Operator-valued frames (2007, background): “Also, several papers in the literature deal with frames in Hilbert C∗-modules, including one by the same authors of this paper [11, 12, 19].”
• Countably generated Hilbert modules, the Kasparov Stabilisation Theorem, and frames in Hilbert modules (2002, methodology): “We became interested in these ideas while studying recent work of Frank and Larson on frames in Hilbert modules, which are, loosely speaking, sequences for which one has a Parseval Identity and a reconstruction formula (see [5, 6]).”
• FRAMES IN HILBERT C*-MODULES AND C*-ALGEBRAS (2000, unknown): “For complementary results to those explained in the present paper we refer to [ 24 , 28].”