منابع مشابه
Projections in Operator Ranges
If H is a Hilbert space, A is a positive bounded linear operator on H and S is a closed subspace of H, the relative position between S and A−1(S⊥) establishes a notion of compatibility. We show that the compatibility of (A,S) is equivalent to the existence of a convenient orthogonal projection in the operator range R(A1/2) with its canonical Hilbertian structure.
متن کاملWeak operator topology, operator ranges and operator equations via Kolmogorov widths
Let K be an absolutely convex infinite-dimensional compact in a Banach space X . The set of all bounded linear operators T on X satisfying TK ⊃ K is denoted by G(K). Our starting point is the study of the closure WG(K) of G(K) in the weak operator topology. We prove that WG(K) contains the algebra of all operators leaving lin(K) invariant. More precise results are obtained in terms of the Kolmo...
متن کاملNumerical Ranges of the Powers of an Operator
The numerical range W (A) of a bounded linear operator A on a Hilbert space is the collection of complex numbers of the form (Av, v) with v ranging over the unit vectors in the Hilbert space. In terms of the location of W (A), inclusion regions are obtained for W (Ak) for positive integers k, and also for negative integers k if A−1 exists. Related inequalities on the numerical radius w(A) = sup...
متن کاملNumerical ranges of an operator on an indefinite inner product space
For n n complex matrices A and an n n Hermitian matrix S, we consider the S-numerical range of A and the positive S-numerical range of A de ned by WS(A) = hAv; viS hv; viS : v 2 I Cn; hv; viS 6= 0
متن کاملEla Numerical Ranges of an Operator on an Indefinite Inner Product Space
For n n complex matrices A and an n n Hermitian matrix S, we consider the S-numerical range of A and the positive S-numerical range of A de ned by WS(A) = hAv; viS hv; viS : v 2 I Cn; hv; viS 6= 0
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1980
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1980-0587947-8