Perturbation by trace class operators
نویسندگان
چکیده
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 ...
متن کاملTrace formulas for stochastic evolution operators: Weak noise perturbation theory
Periodic orbit theory is an effective tool for the analysis of classical and quantum chaotic systems. In this paper we extend this approach to stochastic systems, in particular to mappings with additive noise. The theory is cast in the standard field theoretic formalism, and weak noise perturbation theory written in terms of Feynman diagrams. The result is a stochastic analog of the next-to-lea...
متن کاملPerturbation by Non-Local Operators
Suppose that d ≥ 1 and 0 < β < α < 2. We establish the existence and uniqueness of the fundamental solution q(t, x, y) to a class of (possibly nonsymmetric) non-local operators L = ∆ + S, where Sf(x) := A(d,−β) ∫ R ( f(x+ z)− f(x)−∇f(x) · z1{|z|≤1} ) b(x, z) |z|d+β dz and b(x, z) is a bounded measurable function on R×R with b(x, z) = b(x,−z) for x, z ∈ R. Here A(d,−β) is a normalizing constant ...
متن کاملA Simple Characterization of the Trace - Class of Operators
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.
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 کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1974
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1974-13590-1