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Let ${\mathcal S}$ be the collection of the operator matrices $\left(\begin{smallmatrix} A & C \cr Z & B\end{smallmatrix}\right)$ where the range of $C$ is closed. In this paper, we study the properties of operator matrices in the class ${\mathcal S}$. We first explore various local spectral relations, that is, the property $(\beta)$, decomposable, and the property $(C)$ between the operator matrices in the class $\mathcal{S}$ and their component operators. Moreover, we investigate Weyl and Browder type spectra of operator matrices in the class $\mathcal S$, and as some applications, we provide the conditions for such operator matrices to satisfy $a$-Weyl's theorem and $a$-Browder's theorem, respectively.
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참고문헌 (25)
참고문헌 신청
P. Aiena / 2004 / Fredholm and Local Spectral Theory, with Applications to Multipliers / Kluwer Academic Publishers
Alatancang / 2012 / Perturbation of spectra for a class of 2 2 operator matrices / Acta Math. Appl. Sin. Engl. Ser 28(4):711~720
C. Benhida / 2005 / Spectra of upper triangular operator matrices / Proc. Amer. Math. Soc 133(10):3013~3020
S. W. Brown / 1987 / Hyponormal operators with thick spectra have invariant subspaces / Ann. of Math. 125(1):93~103
X. Cao / 2005 / Weyl's theorem for upper triangular operator matrices / Linear Algebra Appl 402:61~73
Alatancang / 2012 / Perturbation of spectra for a class of 2 2 operator matrices / Acta Math. Appl. Sin. Engl. Ser 28(4):711~720
C. Benhida / 2005 / Spectra of upper triangular operator matrices / Proc. Amer. Math. Soc 133(10):3013~3020
S. W. Brown / 1987 / Hyponormal operators with thick spectra have invariant subspaces / Ann. of Math. 125(1):93~103
X. Cao / 2005 / Weyl's theorem for upper triangular operator matrices / Linear Algebra Appl 402:61~73
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