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
 
