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The aim of this paper is to study the Weyl type-theorems for the orthogonal direct sum $S{\oplus}T$, where S and T are bounded linear operators acting on a Banach space X. Among other results, we prove that if both T and S possesses property ($gb$) and if ${\Pi}(T){\subset}{\sigma}_a(S)$, ${\PI}(S){\subset}{\sigma}_a(T)$, then $S{\oplus}T$ possesses property ($gb$) if and only if ${\sigma}_{SBF^-_+}(S{\oplus}T)={\sigma}_{SBF^-_+}(S){\cup}{\sigma}_{SBF^-_+}(T)$. Moreover, we prove that if T and S both satisfies generalized Browder's theorem, then $S{\oplus}T$ satis es generalized Browder's theorem if and only if ${\sigma}_{BW}(S{\oplus}T)={\sigma}_{BW}(S){\cup}{\sigma}_{BW}(T)$.
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참고문헌 (22)
참고문헌 신청
A. Gupta / 2010 / Generalized a-Weyl's theorem for direct sums / Mat. Vesnik 62 (4) : 265 ~ 270
B. P. Duggal / 2007 / Weyl's theorem for direct sums / Studia Sci. Math. Hungar 44 (2) : 275 ~ 290
D. C. Lay / 1970 / Spectral analysis using ascent, descent, nullity and defect / Math. Ann 184 : 197 ~ 214
H. Heuser / 1982 / Functional Analysis / John Wiley & Sons Inc
K. B. Laursen / 2000 / An Introduction to Local Spectral Theory / Clarendon
B. P. Duggal / 2007 / Weyl's theorem for direct sums / Studia Sci. Math. Hungar 44 (2) : 275 ~ 290
D. C. Lay / 1970 / Spectral analysis using ascent, descent, nullity and defect / Math. Ann 184 : 197 ~ 214
H. Heuser / 1982 / Functional Analysis / John Wiley & Sons Inc
K. B. Laursen / 2000 / An Introduction to Local Spectral Theory / Clarendon
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