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- W170607029 abstract "A semigroup in B(L 2 (X)) is a collection of operators which is closed under multiplication. A band will denote a semigroup of idempo- tents. The question whether a band of infinite-rank operators on an infinite- dimensional Hilbert space is reducible is still unsolved. Here, a negative answer to this problem is given as far as decomposability of a band is con- cerned. Furthermore, conditions leading to decomposability of such bands are discussed. Also, the structure of a maximal nonnegative band of constant rank r is given is under special condition. Borel measure on X. L 2 (X) will denote the Hilbert space of (equivalence classes of) complex-valued measurable functions on X which are square-integrable relative to µ and B(L 2 (X)), the space of all bounded linear operators on L 2 (X). We also assume for simplicity that µ(X) 0 (respectively f > 0) if µ{x 2 X : f(x) < 0} = 0 (respectively µ{x 2 X : f(x) 6 0} = 0). A subspace of L 2 (X) is a norm-closed linear manifold in L 2 (X). A standard subspace of L 2 (X) is a subspace of the form" @default.
- W170607029 created "2016-06-24" @default.
- W170607029 creator A5042063175 @default.
- W170607029 date "2002-01-01" @default.
- W170607029 modified "2023-09-27" @default.
- W170607029 title "DECOMPOSABILITY AND STRUCTURE OF NONNEGATIVE BANDS IN INFINITE DIMENSIONS" @default.
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