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The decomposability of operators relative to two subspaces

100%

Katavolos A., Lambrou M. S., Longstaff W. E.

Studia Mathematica

1993

tom 105

nr 1

25-36

Let M and N be nonzero subspaces of a Hilbert space H satisfying M ∩ N = {0} and M ∨ N = H and let T ∈ ℬ(H). Consider the question: If T leaves each of M and N invariant, respectively, intertwines M and N, does T decompose as a sum of two operators with the same property and each of which, in addition, annihilates one of the subspaces? If the angle between M and N is positive the answer is affirmative. If the angle is zero, the answer is still affirmative for finite rank operators but there are even trace class operators for which it is negative. An application gives an alternative proof that no distance estimate holds for the algebra of operators leaving M and N invariant if the angle is zero, and an analogous result is obtained for the set of operators intertwining M and N.

Completely distributive latices

62%

Lambrou M. S.

Fundamenta Mathematicae

1983

tom 119

nr 3

227-240

Ograniczanie wyników

1 Fundamenta Mathematicae

1 Studia Mathematica

2 Lambrou M. S.

1 Katavolos A.

1 Longstaff W. E.

1 1993

1 1983

Wyniki wyszukiwania

The decomposability of operators relative to two subspaces

Completely distributive latices