hyponormal operator
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2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Salah Mecheri

Abstract The question whether every operator on infinite-dimensional Hilbert space 𝐻 has a nontrivial invariant subspace or a nontrivial hyperinvariant subspace is one of the most difficult problems in operator theory. This problem is open for more than half a century. A subnormal operator has a nontrivial invariant subspace, but the existence of nontrivial invariant subspace for a hyponormal operator 𝑇 still open. In this paper we give an affirmative answer of the existence of a nontrivial hyperinvariant subspace for a hyponormal operator. More generally, we show that a large classes of operators containing the class of hyponormal operators have nontrivial hyperinvariant subspaces. Finally, every generalized scalar operator on a Banach space 𝑋 has a nontrivial invariant subspace.



Filomat ◽  
2019 ◽  
Vol 33 (15) ◽  
pp. 4845-4854
Author(s):  
Muneo Chō ◽  
Dijana Mosic ◽  
Biljana Nacevska-Nastovska ◽  
Taiga Saito

In this paper, we introduce a square hyponormal operator as a bounded linear operator T on a complex Hilbert space H such that T2 is a hyponormal operator, and we investigate some basic properties of this operator. Under the hypothesis ?(T) ? (-?(T)) ? {0}, we study spectral properties of a square hyponormal operator. In particular, we show that if z and w are distinct eigen-values of T and x,y ? H are corresponding eigen-vectors, respectively, then ?x,y? = 0. Also, we define nth hyponormal operators and present some properties of this kind of operators.



2019 ◽  
pp. 155-168
Author(s):  
Yongji ng Duan ◽  
Shi ao Pang ◽  
S yu Wang
Keyword(s):  


2019 ◽  
pp. 1163-1171
Author(s):  
Abderrahim Baghdad ◽  
Mohamed Chraibi Kaadoud


2016 ◽  
Vol 24 (1) ◽  
pp. 65-70
Author(s):  
Jae Won Lee ◽  
In Ho Jeon
Keyword(s):  


2014 ◽  
Vol 288 (5-6) ◽  
pp. 670-679
Author(s):  
M. H. M. Rashid


2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Fei Zuo ◽  
Junli Shen

We provide some conditions for2×2operator matrices whose diagonal entries areM-hyponormal operators to be subscalar. As a consequence, we obtain that Weyl type theorem holds for such operator matrices.



2012 ◽  
Vol 262 (9) ◽  
pp. 3946-3980 ◽  
Author(s):  
Zenon Jan Jabłoński ◽  
Il Bong Jung ◽  
Jan Stochel
Keyword(s):  


2012 ◽  
Vol 02 (06) ◽  
pp. 419-422
Author(s):  
Md. Ilyas ◽  
Reyaz Ahmad
Keyword(s):  


2011 ◽  
Vol 31 (1) ◽  
pp. 93-101
Author(s):  
Yang Changsen ◽  
Ding Yanfeng
Keyword(s):  


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