TAILIEUCHUNG - Invariant subspaces of weakly compact-friendly operators

We prove that if a non-zero weakly compact-friendly operator B on a Banach lattice with topologically full center is locally quasi-nilpotent, then the super right-commutant [B of B has a non-trivial closed invariant ideal. An example of a weakly compact-friendly operator which is not compact-friendly is also provided. | Turk J Math 36 (2012) , 291 – 295. ¨ ITAK ˙ c TUB doi: Invariant subspaces of weakly compact-friendly operators Mert C ¸ a˘glar and Tun¸c Mısırlıo˘glu Abstract We prove that if a non-zero weakly compact-friendly operator B on a Banach lattice with topologically full center is locally quasi-nilpotent, then the super right-commutant [B of B has a non-trivial closed invariant ideal. An example of a weakly compact-friendly operator which is not compact-friendly is also provided. Key Words: Banach lattice, topologically full center, invariant subspace, weakly compact-friendly 1. Introduction Weakly compact-friendly operators have been defined in [3] as a natural extension of compact-friendly operators. Therein, it was shown [3, Theorem ], among others, that a locally quasi-nilpotent weakly compactfriendly operator on a Banach lattice has a non-trivial closed invariant ideal. The purpose of this note is to extend some results in [1] and [4] in the setting of weakly compact-friendly operators on Banach lattices with topologically full center. In doing so, we also provide an example of a weakly compact-friendly operator which is not compact-friendly. Throughout the paper E denotes an infinite-dimensional Banach lattice. As usual, L(E) and L(E)+ stand, respectively, for the algebra of all bounded linear operators and the collection of all positive operators on E . For a positive operator B on a Banach lattice E , the super right-commutant [B of B is defined by [B := {A ∈ L(E)+

• Toán học
• Banach lattice
• Topologically full center
• Invariant subspace
• Weakly compact friendly
• Locally quasi nilpotent
• Sự tồn tại nghiệm
• Toán tử lattice
• Nguyên lí điểm bất động Banach
• Phương trình vi tích phân phân thứ
• Tuyến tính dạng Lattice
• báo cáo khoa học
• báo cáo hóa học
• công trình nghiên cứu về hóa học
• tài liệu về hóa học
• cách trình bày báo cáo