Abstract: When A鈭圔(H1), B鈭圔(H2) and C鈭圔(H3) are given, we denote by M(D,E,F) an operator, acting on the Hilbert space H1H2H3, of the form M(D, E, F)= . In this paper, we give the necessary and sufficient condition for M(D,E,F) to be upper semi-Fredholm (lower semi-Fredholm) operator for some D鈭圔(H2,H1), E鈭圔(H3,H1), F鈭圔(H3,H2). Weyl type theorems are liable to fail for 2脳2 operator matrices. In this paper, we also explore how Weyl's theorem, Browder's theorem, 伪-Weyl's theorem and 伪-Browder's theorem survive for 3脳3 upper triangular operator matrices on the Hilbert space.

鎽樿锛� 璁続鈭圔(H1),B鈭圔(H2),C鈭圔(H3)涓虹粰瀹氱殑涓変釜绠楀瓙,鐢∕(D,E,F)= 琛ㄧず涓�涓綔鐢ㄥ湪H1(?)H2(?)H3涓婄殑3脳3绠楀瓙鐭╅樀锛庢湰鏂囬鍏堢粰鍑哄瓨鍦ㄧ畻瀛怐鈭圔(H2,H1),E鈭圔(H3,H1),F鈭圔(H3,H2),浣垮緱M(D,E,F)涓轰笂鍗奆redholm绠楀瓙(涓嬪崐Fredholm绠楀瓙)鐨勫厖瑕佹潯浠讹紟鍚屾椂鐮旂┒浜�3脳3绠楀瓙鐭╅樀 M(D,E,F)鐨刉eyl瀹氱悊,伪-Weyl瀹氱悊,Browder瀹氱悊鍜屛�-Browder瀹氱悊锛�

鍏抽敭璇�: Browder瀹氱悊, 璋�, Weyl瀹氱悊