منابع مشابه
Trace class operators and Hilbert-Schmidt operators
If X,Y are normed spaces, let B(X,Y ) be the set of all bounded linear maps X → Y . If T : X → Y is a linear map, I take it as known that T is bounded if and only if it is continuous if and only if E ⊆ X being bounded implies that T (E) ⊆ Y is bounded. I also take it as known that B(X,Y ) is a normed space with the operator norm, that if Y is a Banach space then B(X,Y ) is a Banach space, that ...
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The trace-class (Tc) of operators on a Hilbert space is characterized in terms of existence of certain centralizers. KEY WO.Rt)S., AI. PHPASES. 1980 MATHEMATICS SUBJECT CLASSIFICATION CODE3. 47BI0, 46K15.
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In the present article, we investigate a possibility of a real-valued map on the space of tuples of commuting trace-class self-adjoint operators, which behaves like the usual trace map on the space of trace-class linear operators. It turns out that such maps are related with continuous group homomorphisms from the Milnor’s K-group of the real numbers into the additive group of real numbers. Usi...
متن کاملTrace Class Conditions for Functions of Schrödinger Operators
We consider the difference f(−∆+V )−f(−∆) of functions of Schrödinger operators in L(R) and provide conditions under which this difference is trace class. We are particularly interested in non-smooth functions f and in V belonging only to some L space. This is motivated by applications in mathematical physics related to Lieb–Thirring inequalities. We show that in the particular case of Schrödin...
متن کاملLocal Derivations on Algebras of Measurable Operators
The paper is devoted to local derivations on the algebra S(M, τ) of τ measurable operators affiliated with a von Neumann algebra M and a faithful normal semi-finite trace τ. We prove that every local derivation on S(M, τ) which is continuous in the measure topology, is in fact a derivation. In the particular case of type I von Neumann algebras they all are inner derivations. It is proved that f...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1979
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1979-0512062-0