Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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Bull. Korean Math. Soc. 2014; 51(6): 1727-1733

Printed November 30, 2014

https://doi.org/10.4134/BKMS.2014.51.6.1727

Copyright © The Korean Mathematical Society.

A note on $k$-hyperreflexivity of Toeplitz-harmonic subspaces

Piotr Budzy\'nski, Kamila Piwowarczyk, and Marek Ptak

Uniwersytet Rolniczy w Krakowie, Uniwersytet Rolniczy w Krakowie, Uniwersytet Rolniczy w Krakowie

Abstract

The 2-hyperreflexivity of Toeplitz-harmonic type subspace generated by an isometry or a quasinormal operator is shown. The $k$-hyperreflexivity of the tensor product $\ss\otimes \vv$ of a $k$-hyperreflexive decomposable subspace $\ss$ and an abelian von Neumann algebra $\vv$ is established.

Keywords: $k$-hyperreflexive subspace, direct integral, tensor product, isometry, quasinormal operator

MSC numbers: Primary 47L05; Secondary 47L75