PENTAGON SUBSPACE LATTICES ON BANACH SPACES
PENTAGON SUBSPACE LATTICES ON BANACH SPACES
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DOI：
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发表时间：
2001
影响因子：
0.8
通讯作者：
A. Katavolos;M. S. Lambrou;W. E. Longstaff
中科院分区：
文献类型：
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作者：
A. Katavolos;M. S. Lambrou;W. E. Longstaff
如果K，L和M是Banach空间X的（闭）子空间-满足K \ M = (0),K _ L = X和L M，则P = {(0)，K，L，M，X}是X上的五边形子空间格。如果P1和P2是五边形，则每（代数）同构':AlgP1 ！AlgP2是准空间的。AlgP的有限秩子代数的sot闭包为{t2 AlgP: T(M) L}。在可分希尔伯特空间H上，每一个正的、内射的、不可逆的算子A和每一个满足M \ Ran(A) =(0)的非零子空间M都得到一个五边形P（A；M）。对于可逆算子t2 B(H), AlgP（A；M）和AlgP（B；N）是空间同构的当且仅当T Ran(A) = Ran(B)和T(M) = N。如果A(A)是使Ran(A)不变的算子集合，则每同构':A(A) ！A(B)由满足T Ran(A) = Ran(B)的可逆算子T实现。
If K,L and M are (closed) subspaces of a Banach space X sat- isfying K \ M = (0), K _ L = X and L M, then P = {(0),K,L,M,X} is a pentagon subspace lattice on X. If P1 and P2 are pentagons, every (al- gebraic) isomorphism ' : AlgP1 ! AlgP2 is quasi-spatial. The SOT-closure of the fin- ite rank subalgebra of AlgP is {T 2 AlgP : T(M) L}. On separable Hilbert space H every positive, injective, non-invertible operator A and every non-zero subspace M satisfying M \ Ran(A) = (0) give rise to a pentagon P(A;M). AlgP(A;M) and AlgP(B;N) are spatially isomorphic if and only if T Ran(A) = Ran(B) and T(M) = N for an invertible operator T 2 B(H). If A(A) is the set of operators leaving Ran(A) invariant, every isomorphism ' : A(A) ! A(B) is implemented by an invertible operator T satisfying T Ran(A) = Ran(B).