Spectral shift function, amazing and multifaceted
نویسندگان
چکیده
منابع مشابه
Krein Spectral Shift Function
A b s t r a c t . Let ~A,B be the Krein spectral shift function for a pair of operators A, B, with C = A B trace class. We establish the bound f F(I~A,B()~)I ) d,~ <_ f F ( 1 5 1 c l , o ( ) , ) l ) d A = ~ [F(j) F ( j 1 ) ] # j ( C ) , j= l where F is any non-negative convex function on [0, oo) with F(O) = 0 and #j (C) are the singular values of C. The choice F(t) = t p, p > 1, improves a rece...
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We extend the concept of Lifshits–Krein spectral shift function associated with a pair of self-adjoint operators to the case of pairs of (admissible) operators that are similar to self-adjoint operators. An operator H is called admissible if: (i) there is a bounded operator V with a bounded inverse such that H = V −1 HV for some self-adjoint operator H; (ii) the operators H and H are resolvent ...
متن کاملKrĕin’s Trace Formula and the Spectral Shift Function
Let A,B be two selfadjoint operators whose difference B −A is trace class. Krĕın proved the existence of a certain function ξ ∈ L1(R) such that tr[f (B)−f(A)] = ∫ Rf (x)ξ(x)dx for a large set of functions f . We give here a new proof of this result and discuss the class of admissible functions. Our proof is based on the integral representation of harmonic functions on the upper half plane and a...
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ژورنال
عنوان ژورنال: Integral Equations and Operator Theory
سال: 1998
ISSN: 0378-620X,1420-8989
DOI: 10.1007/bf01238218