Strongly irreducible operators on Banach spaces

2011 ◽  
Vol 28 (4) ◽  
pp. 727-740 ◽  
Author(s):  
Yun Nan Zhang ◽  
Huai Jie Zhong
Keyword(s):  
Banach Spaces ◽  
Strongly Irreducible Operators ◽  
Strongly Irreducible

THE STRONG IRREDUCIBILITY OF A CLASS OF COWEN–DOUGLAS OPERATORS ON BANACH SPACES

2016 ◽  
Vol 94 (3) ◽  
pp. 479-488
Author(s):  
LIQIONG LIN ◽  
YUNNAN ZHANG
Keyword(s):  
Banach Spaces ◽  
Open Subset ◽  
Hilbert Spaces ◽  
Strongly Irreducible ◽  
Connected Open Subset ◽  
Strong Irreducibility

Let ${\mathcal{B}}_{n}(\unicode[STIX]{x1D6FA})$ be the set of Cowen–Douglas operators of index $n$ on a nonempty bounded connected open subset $\unicode[STIX]{x1D6FA}$ of $\mathbb{C}$. We consider the strong irreducibility of a class of Cowen–Douglas operators ${\mathcal{F}}{\mathcal{B}}_{n}(\unicode[STIX]{x1D6FA})$ on Banach spaces. We show ${\mathcal{F}}{\mathcal{B}}_{n}(\unicode[STIX]{x1D6FA})\subseteq {\mathcal{B}}_{n}(\unicode[STIX]{x1D6FA})$ and give some conditions under which an operator $T\in {\mathcal{F}}{\mathcal{B}}_{n}(\unicode[STIX]{x1D6FA})$ is strongly irreducible. All these results generalise similar results on Hilbert spaces.

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