When A ∈ B（H） and B ∈ B（K） are given, we denote by Me the operator matrix acting on the infinite dimensional separable Hilbert space H ＋ K of the form Me = （ A C O B）. In this paper, a necessary and sufficien...When A ∈ B（H） and B ∈ B（K） are given, we denote by Me the operator matrix acting on the infinite dimensional separable Hilbert space H ＋ K of the form Me = （ A C O B）. In this paper, a necessary and sufficient condition for Me to be left Fredholm for some C ∈ F（K, H） （C ∈ Inv（K, H）） is given, where F（K,H） and Inv（K, H） denote respectively, the set of Fredholm operators and the set of invertible operators of B（K, H）. In addition, we give a necessary and sufficient condition for Me to be left Fredholm for all C ∈ Inv（K, H）.展开更多
文摘When A ∈ B（H） and B ∈ B（K） are given, we denote by Me the operator matrix acting on the infinite dimensional separable Hilbert space H ＋ K of the form Me = （ A C O B）. In this paper, a necessary and sufficient condition for Me to be left Fredholm for some C ∈ F（K, H） （C ∈ Inv（K, H）） is given, where F（K,H） and Inv（K, H） denote respectively, the set of Fredholm operators and the set of invertible operators of B（K, H）. In addition, we give a necessary and sufficient condition for Me to be left Fredholm for all C ∈ Inv（K, H）.
