Tridiagonal shifts as compact + isometry

Article Type

Research Article

Publication Title

Archiv der Mathematik

Abstract

Let {an}n≥0 and {bn}n≥0 be sequences of scalars. Suppose an≠ 0 for all n≥ 0. We consider the tridiagonal kernel (also known as band kernel with bandwidth one) as k(z,w)=∑n=0∞((an+bnz)zn)((an+bnw)wn)¯(z,w∈D),where D= { z∈ C: | z| < 1 }. Denote by Mz the multiplication operator on the reproducing kernel Hilbert space corresponding to the kernel k. Assume that Mz is left-invertible. We prove that Mz= compact + isometry if and only if |bnan-bn+1an+1|→0 and |anan+1|→1.

First Page

507

Last Page

518

DOI

10.1007/s00013-022-01780-8

Publication Date

11-1-2022

Comments

Open Access, Green

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