منابع مشابه
A Note on Quadratic Maps for Hilbert Space Operators
In this paper, we introduce the notion of sesquilinear map on Β(H) . Based on this notion, we define the quadratic map, which is the generalization of positive linear map. With the help of this concept, we prove several well-known equality and inequality...
متن کاملCompact Operators on Hilbert Space
Among all linear operators on Hilbert spaces, the compact ones (defined below) are the simplest, and most imitate the more familiar linear algebra of finite-dimensional operator theory. In addition, these are of considerable practical value and importance. We prove a spectral theorem for self-adjoint operators with minimal fuss. Thus, we do not invoke broader discussions of properties of spectr...
متن کاملHankel Operators on Hilbert Space
commonly known as Hilbert's matrix, determines a bounded linear operator on the Hilbert space of square summable complex sequences. Infinite matrices which possess a similar form to H, namely those that are 'one way infinite' and have identical entries in cross diagonals, are called Hankel matrices, and when these matrices determine bounded operators we have Hankel operators, the subject of thi...
متن کاملintersection theory and operators in Hilbert space
For an operator of a certain class in Hilbert space, we introduce axioms of an abstract intersection theory, which we prove to be equivalent to the Riemann Hypothesis concerning the spectrum of that operator. In particular if the nontrivial zeros of the Riemann zeta-function arise from an operator of this class, the original Riemann Hypothesis is equivalent to the existence of an abstract inter...
متن کاملOn Commutators of Operators on Hilbert Space
1. In this note we first generalize a result of P. R. Halmos [3] concerning commutators of (bounded ) operators on Hubert space. Then we obtain some partial results on a problem of commutators in von Neumann algebras which is closely related to another problem raised by Halmos in [4]. Let 3C be any (infinite-dimensional) Hubert space, and let £(3C) denote the algebra of all bounded operators on...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1979
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1979-0534392-9