Nihonkai Mathematical Journal

Common invariant subspaces of two doubly commuting operators on $\ell^2 \otimes \mathbb{C}^2$

Takahiko Nakazi and Michio Seto

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Abstract

In this paper, we study common invariant subspaces of $\mathbb{T}$ and $\mathbb{S}$ on $\ell^2 \otimes \mathbb{C}^2$ where $\mathbb{T} = T \otimes I_{\mathbb{C}^2}$ and $\mathbb{S} = I_{\ell^2} \otimes S$. We describe such invariant subspaces using $T$ and $S$.

Article information

Source
Nihonkai Math. J., Volume 20, Number 2 (2009), 127-137.

Dates
First available in Project Euclid: 26 March 2010

Permanent link to this document
https://projecteuclid.org/euclid.nihmj/1269610689

Mathematical Reviews number (MathSciNet)
MR2650464

Zentralblatt MATH identifier
1200.47012

Subjects
Primary: 47A15: Invariant subspaces [See also 47A46] 47A80: Tensor products of operators [See also 46M05]

Keywords
$l^1$ $F$-space Hardy space Smirnov class

Citation

Nakazi, Takahiko; Seto, Michio. Common invariant subspaces of two doubly commuting operators on $\ell^2 \otimes \mathbb{C}^2$. Nihonkai Math. J. 20 (2009), no. 2, 127--137. https://projecteuclid.org/euclid.nihmj/1269610689


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