Asymptotic Moore-Penrose inversion of Toeplitz operators

✍ Scribed by Bernd Silbermann

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 567 KB
• Volume: 256
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/s0024-3795(96)00043-2

✦ Synopsis

We give the complete solution of a problem which reads in its simplest form as follows: Let T(a) be a block Toeplitz operator with piecewise continuous generating function and A n := T,(a) be the finite sections of this operator. Describe all sequences {Bn} belonging to the algebra ,~' which is generated by all the sequences {T~(a)} with a piecewise continuous, and fulfilling the conditions { A n B n A n -A n} G, {BnAnB n -Bn} ~ G, {(BnA~)* -BnA~} ~ G, {(AnBn)* -AnB,~} E G, where G cd denotes the collection of all sequences (C n) with IICnll ~ 0 as n tends to infinity, and T(a) is supposed to be Fredholm.