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The intersection of left (right) spectra of 2 × 2 upper triangular operator matrices

✍ Scribed by Yuan Li; Xiu-Hong Sun; Hong-Ke Du

Publisher
Elsevier Science
Year
2006
Tongue
English
Weight
141 KB
Volume
418
Category
Article
ISSN
0024-3795

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✦ Synopsis

When A ∈ B(H) and B ∈ B(K) are given, we denote by M C the operator matrix acting on the infinite-

. In this paper, for given A and B, the sets C∈B l (K,H) σ l (M C ), C∈Inv(K,H) σ l (M C ) and C∈Inv(K,H) σ l (M C ) are determined, where σ l (T ), B l (K, H) and Inv(K, H) denote, respectively, the left spectrum of an operator T, the set of all the left invertible operators and the set of all the invertible operators from K into H.

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