Open AccessAlgebraic extension of $\mathcal{A}^{*}_{n}$ operator
Author(s) -
Ilmi Hoxha,
Naim L. Braha
Publication year - 2021
Publication title -
boletim da sociedade paranaense de matemática
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.347
H-Index - 15
eISSN - 2175-1188
pISSN - 0037-8712
DOI - 10.5269/bspm.43345
Subject(s) - operator (biology) , extension (predicate logic) , algebraic number , mathematics , algebraic extension , combinatorics , discrete mathematics , algebra over a field , pure mathematics , mathematical analysis , computer science , differential algebraic equation , ordinary differential equation , biochemistry , chemistry , repressor , transcription factor , gene , programming language , differential equation
$T\in L(H_{1}\oplus H_{2})$ 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.