Algebraic extension of $\mathcal{A}^{*}_{n}$ operator
Abstract
$T\in L(H_{1}\oplus H_{2})$ is said to be an algebraic extension of a $\mathcal{A}^{*}_{n}$ operator if $$ T = \begin{pmatrix} T_{1} & T_{2} \\
O & T_{3} \end{pmatrix} $$ is an operator matrix on $H_{1}\oplus H_{2}$, where $T_{1}$ is a $\mathcal{A}^{*}_{n}$ operator and $T_{3}$ is a algebraic.
In this paper, we study basic and spectral properties of an algebraic extension of a $\mathcal{A}^{*}_{n}$ operator. We show that every algebraic extension of a $\mathcal{A}^{*}_{n}$ operator has SVEP, is polaroid and satisfies Weyl's theorem.
Downloads
References
Aiena, P., Semi-Fredholm operators, perturbations theory and localized SVEP, Merida, Venezuela (2007).
Aiena, P.; Aponte, E.; Bazan, E., Weyl type theorems for left and right polaroid operators, Integral Equations Oper. Theory 66, 1-20, (2010). https://doi.org/10.1007/s00020-009-1738-2
Aiena, P.; Pe˜na, P., Variations on Weyls theorem, J. Math. Anal. Appl. 324 (1), 566-579, (2006). https://doi.org/10.1016/j.jmaa.2005.11.027
Aiena, P., Fredholm and Local Spectral Theory with Applications to Multipliers, Kluwer, (2004).
Cao, X. H., Analytically Class A operators and Weyl's theorem, J. Math. Anal. Appl. 320, 795-803, (2006). https://doi.org/10.1016/j.jmaa.2005.07.056
Foias, C.; Frazho, A.E., The Commutant Lifting Approach to Interpolation Problem, Basel, Birkh¨auser Verlag, (1990). https://doi.org/10.1007/978-3-0348-7712-1
Hansen, F., An operator inequality, Math. Ann. 246, 249-250, (1980). https://doi.org/10.1007/BF01371046
Heuser, H., Functional Analysis, Marcel Dekker, New York, (1982).
Hoxha, I.; Braha, N. L., On k-Quasi Class A∗n Operators , Bulletin of Mathematical Analysis and Applications, Volume 6 Issue 1, Pages 23-33, (2014).
Han, J. K.; Lee, H. Y.; Lee, W. Y., Invertible completions of 2 × 2 upper triangular operator matrices Proceedings of the American Mathematical Society, vol. 128, no. 1, pp. 119-123, (2000). https://doi.org/10.1090/S0002-9939-99-04965-5
Lee, W. Y.; Lee, S. H., A spectral mapping theorem for the Weyl spectral, Glasgow Math. J. 38, no. 1, 61-64, (1996). https://doi.org/10.1017/S0017089500031268
Rashid, M. H. M., Property (ω) and quasi class (A, k) operators, Rev. Un. Mat. Argentina, Vol. 52, Nu 1, 133-142, (2011).
Copyright (c) 2021 Boletim da Sociedade Paranaense de Matemática
This work is licensed under a Creative Commons Attribution 4.0 International License.
When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).
The journal utilize the Creative Common Attribution (CC-BY 4.0).
