Naslov
Frames and outer frames for Hilbert C*-modules

Autori
Arambašić, Ljiljana ; Bakić, Damir

Izvornik
Linear and multilinear algebra (0308-1087) 65 (2017), 2; 381-431

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Hilbert C*-module ; frame ; outer frame ; strict frame ; multiplier module

Sažetak
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 l^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 obtain new results on dual frames, frame perturbations, tight approximations of frames and finite extensions of Bessel sequences.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA