Perturbation of Operators and Applications to Frame Theory

Ole Christensen; P. Casazza

Perturbation of Operators and Applications to Frame Theory

Research output: Book/Report › Report › Research › peer-review

Abstract

A celebrated classical result states that an operator Uon a Banach space is invertible, if it is close enough to the identityoperator I. Here we showthat U actually is invertible under a much weaker condition. As anapplication we prove new theorems concerning stability of frames (andframe-like decompositions) under perturbation in both Hilbert spacesand Banach spaces.

Original language	English

Number of pages	22
Publication status	Published - 1996

OpenUrl availability

Full text

Cite this

@book{3845b2d217b0494fb0cbe52ae0e861ae,

title = "Perturbation of Operators and Applications to Frame Theory",

abstract = "A celebrated classical result states that an operator Uon a Banach space is invertible, if it is close enough to the identityoperator I. Here we showthat U actually is invertible under a much weaker condition. As anapplication we prove new theorems concerning stability of frames (andframe-like decompositions) under perturbation in both Hilbert spacesand Banach spaces.",

author = "Ole Christensen and P. Casazza",

year = "1996",

language = "English",

}

TY - RPRT

T1 - Perturbation of Operators and Applications to Frame Theory

AU - Christensen, Ole

AU - Casazza, P.

PY - 1996

Y1 - 1996

N2 - A celebrated classical result states that an operator Uon a Banach space is invertible, if it is close enough to the identityoperator I. Here we showthat U actually is invertible under a much weaker condition. As anapplication we prove new theorems concerning stability of frames (andframe-like decompositions) under perturbation in both Hilbert spacesand Banach spaces.

AB - A celebrated classical result states that an operator Uon a Banach space is invertible, if it is close enough to the identityoperator I. Here we showthat U actually is invertible under a much weaker condition. As anapplication we prove new theorems concerning stability of frames (andframe-like decompositions) under perturbation in both Hilbert spacesand Banach spaces.

M3 - Report

BT - Perturbation of Operators and Applications to Frame Theory

ER -