Title




Some properties of the KMSFunction
 
Author




 
Abstract




Let, for j = 0, 1, Hj = HJ* greater than or equal to w(j) > infinity, be a selfadjoint operator in the Hilbert spaces Hj. Let T : H1 > H0 be a linear operator with domain in H1 and range in H0. Let Vj(t) = exp(tH(j)), t greater than or equal to 0, be the strongly continuous semigroup generated by Hj, j = 0, 1 If the operators (aI + H0) V0 (t(0)) T (aI + H1)(1) and (aI + H0)(1) T (aI + H1) V1 (t(0)) are compact, (HillbertSchmidt, Trace class), then so is the operator integral (t0)(0) V0(u)TV1(T0u)du. The result is applicable if T = JH(1)  H(0)J, where J : H1 > H0 is a bounded linear (identification) operator. In this case integral (t0)(0) V0(u)TV1(t(0)  u)du = V0(t(0)) J  JV(1) (t(0)); i.e. the difference of the semigroups. Some convergence and approximation results are presented as well. For example the operator integral (t0)(0) V0(u)TV1(t(0)  u)du is expressed in terms of the operator t(0)V(0) (t(0)/2) TV1 (t(0)/2). 
 
Language




English
 
Source (journal)




Lecture notes in pure and applied mathematics.  New York
 
Publication




New York
:
2001
 
ISSN




00758469
 
Volume/pages




215
(2001)
, p. 453472
 
ISI




000169067400038
 
