Browder–Weyl theorems, tensor products and multiplications

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• 作者：B.P. Duggal
• 关键词：Banach space ; Browder's theorem ; Weyl's theorem ; Single-valued extension property ; Polaroid operator ; Hereditarily normaloid operators
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2009
• 出版时间：15 November 2009
• 年：2009
• 卷：359
• 期：2
• 页码：631-636
• 全文大小：178 K

文摘

A Banach space operator satisfies Browder's theorem if the complement of the Weyl spectrum σ_w(T) of T in σ(T) equals the set of Riesz points of T; T is polaroid if the isolated points of σ(T) are poles (no restriction on rank) of the resolvent of T. Let Φ(T) denote the set of Fredholm points of T. Browder's theorem transfers from to S=L_AR_B (resp., S=AB) if and only if A and B^* (resp., A and B) have SVEP at points μΦ(A) and νΦ(B) for which λ=μνσ_w(S). If A and B are finitely polaroid, then the polaroid property transfers from and to L_AR_B; again, restricting ourselves to the completion of in the projective topology, if A and B are finitely polaroid, then the polaroid property transfers from and to AB.