2 &times; 2-上三角算子矩阵谱的Fredholm扰动

doi:10.12386/A2011sxxb0059

鏁板瀛︽姤鈥衡�� 2011, Vol. 54 鈥衡�� Issue (4): 581-590.DOI: 10.12386/A2011sxxb0059

鈥� 璁烘枃鈥� 涓婁竴绡� 涓嬩竴绡�

2 × 2-涓婁笁瑙掔畻瀛愮煩闃佃氨鐨凢redholm鎵板姩

寮犱笘鑺�^1,2, 閽熸��鏉�², 姝︿繆寰�¹

1. 娴欐睙澶у鏁板绯� 鏉窞 310027;
2. 绂忓缓甯堣寖澶у鏁板涓庤绠楁満绉戝瀛﹂櫌绂忓窞 350007

鏀剁鏃ユ湡:2009-07-02 淇洖鏃ユ湡:2011-01-06 鍑虹増鏃ユ湡:2011-07-15 鍙戝竷鏃ユ湡:2011-07-15
鍩洪噾璧勫姪:
鍥藉鑷劧绉戝鍩洪噾(10771034, 10771191,10471124);绂忓缓鐪佽嚜鐒剁瀛﹀熀閲�(Z0511019, S0650009)

Fredholm Perturbation of Spectra of 2 × 2-Upper Triangular Matrices

Shi Fang ZHANG^1,2, Huai Jie ZHONG², Jun De WU¹

1. Department of Mathematics, Zhejiang University, Hangzhou 310027, P. R. China;
2. School of Mathematics and Computer Science, Fujian Normal University, Fuzhou 350007, P. R. China,

Received:2009-07-02 Revised:2011-01-06 Online:2011-07-15 Published:2011-07-15

鎽樿/Abstract

鎽樿锛� 璁�H鍜�K鏄鏃犵┓缁村彲鍒咹ilbert绌洪棿, A ∈ B(H), B ∈ B(K), C ∈ B(K, H)涓�M_C=(₀^A_B^C). 鏈枃缁欏嚭浜嗕笂涓夎绠楀瓙鐭╅樀M_C鐨� Weyl 璋便�佹湰鎬ц氨銆佽氨銆佸乏璋便�佸彸璋便�佷笅鍗婃湰鎬ц氨銆佷笅鍗� Weyl璋� 鍜屼笂鍗奧eyl璋辩殑Fredholm 鎵板姩鐨勫畬鍏ㄥ埢鐢�.

鍏抽敭璇�: Banach绌洪棿, 涓婁笁瑙掔畻瀛愮煩闃�, 璋�, 鎵板姩

Abstract: Let H and K be complex infinite dimensional separable Hilbert spaces, A ∈ B(H), B ∈ B(K), C ∈ B(K,H) and M_C = (₀^A_B^C). In this paper, we characterize completely the Fredholm perturbation for the Weyl spectrum, essential spectrum, spectrum, left spectrum, right spectrum, lower semi-Fredholm spectrum, lower semi-Weyl spectrum and upper semi-Weyl spectrum of the upper triangular operator matrices M_C.

Key words: Banach spaces, upper-triangular operator matrices, spectra, perturbation

涓浘鍒嗙被鍙�:

O177.2

寮犱笘鑺�, 閽熸��鏉�, 姝︿繆寰�. 2 × 2-涓婁笁瑙掔畻瀛愮煩闃佃氨鐨凢redholm鎵板姩[J]. 鏁板瀛︽姤, 2011, 54(4): 581-590.

Shi Fang ZHANG, Huai Jie ZHONG, Jun De WU. Fredholm Perturbation of Spectra of 2 × 2-Upper Triangular Matrices[J]. Acta Mathematica Sinica, Chinese Series, 2011, 54(4): 581-590.

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閾炬帴鏈枃: https://actamath.cjoe.ac.cn/Jwk_sxxb_cn/CN/10.12386/A2011sxxb0059

https://actamath.cjoe.ac.cn/Jwk_sxxb_cn/CN/Y2011/V54/I4/581

鍙傝�冩枃鐚�

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2 × 2-涓婁笁瑙掔畻瀛愮煩闃佃氨鐨凢redholm鎵板姩

Fredholm Perturbation of Spectra of 2 × 2-Upper Triangular Matrices

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