Published in Forum Mathematicum
A commuting triple of Hilbert space operators ( A , B , P ) {(A,B,P)} , for which the closed tetrablock 𝔼 ¯ {\overline{\mathbb{E}}} is a spectral set, is called a tetrablock-contraction or simply an 𝔼 {\mathbb{E}} -contraction, where 𝔼 = { ( x 1 , x 2 , x 3 ) ∈ ℂ 3 : 1 - x 1 z - x 2 w + x 3 z w ≠ 0 whenever | z | ≤ 1 and | w | ≤ 1 }...
Published in Open Mathematics
In this paper, we study the structures of the invariant subspaces under the action of orthogonal group O 2 ν ( F q , S ) {O}_{2\nu }\left({F}_{q},S) . In particular, we give a detailed description of 2-codimensional invariant subspaces. Moreover, we show that the height of transfer ideal Im ( Tr O 2 ν ( F q , S ) ) {\rm{Im}}({{\rm{Tr}}}^{{O}_{2\nu ...
Published in Annals of Functional Analysis
In this article, first, we study the spectral properties of operators which attain their norm on every reducing subspace and then we study the structure of normal and quasinormal operators in this class. At the end we give a description of paranormal operators whose adjoint is also paranormal. This gives a direct proof of the fact that an operator ...
Published in Advances in Operator Theory
The pseudospectrum and condition spectrum are two essential generalizations of the spectrum. In this paper, we define the eigenvector corresponding to pseudospectral value and eigenvector corresponding to the condition spectral value of a bounded operator on a separable Hilbert space. The eigenvector corresponding to a pseudospectral value (or cond...
Published in Georgian Mathematical Journal
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...
Published in Banach Journal of Mathematical Analysis
In the present paper, we first study the wandering subspace property of the shift operator on the Ia\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$I_{a}$$\end{document...
Published in Journal of Inequalities and Applications
In this paper, we focus on a 2×2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$2 \times 2$\end{document} operator matrix Tϵk\documentclass[12pt]{minimal} \usepackage{am...
Published in Integral Equations and Operator Theory
Inspired by Szegö’s theorem, this paper focuses on characterizing cyclic vectors and outer functions in H2(D2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H^2({\math...
Published in Banach Journal of Mathematical Analysis
In this article we refer to operators T on a Hilbert space H\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {H}$$\end{document} which can be lifted to some 3-i...
Published in Results in Mathematics
Let G be an abelian semigroup of matrices on Kn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {K}}^{n}$$\end{document} (n≥1\documentclass[12pt]{minimal} \usep...
