A Hilbert Space Problem Book.

1984 ◽  
Vol 91 (9) ◽  
pp. 592
Author(s):  
Peter Fillmore ◽  
Nigel Higson ◽  
Paul R. Halmos
1984 ◽  
Vol 91 (9) ◽  
pp. 592-594
Author(s):  
Peter Fillmore ◽  
Nigel Higson

1989 ◽  
Vol 73 (465) ◽  
pp. 259
Author(s):  
Philip Maher ◽  
P. R. Halmos

1968 ◽  
Vol s1-43 (1) ◽  
pp. 565-565
Author(s):  
F. Smithies

1971 ◽  
Vol 78 (5) ◽  
pp. 525-527
Author(s):  
G. G. Johnson
Keyword(s):  

1989 ◽  
Vol 31 (2) ◽  
pp. 219-229
Author(s):  
Mícheál Ó Searcóid

We consider the hypothesis that an operator T on a given Banach space can always be perturbed by a compact operator K in such a way that, whenever a complex number A is in the semi-Fredholm region of T + K, then T + K – λ is either bounded below or surjective. The hypothesis has its origin in the work of West [11], who proved it for Riesz operators on Hilbert space. In this paper, we reduce the general Banach space problem to one of considering only operators of a special type, operators which are, in a spectral sense, natural generalizations of the Riesz operators studied by West.


1971 ◽  
Vol 78 (5) ◽  
pp. 525
Author(s):  
G. G. Johnson
Keyword(s):  

2003 ◽  
Vol 44 (4) ◽  
pp. 485-500 ◽  
Author(s):  
P. G. Howlett ◽  
C. E. M. Pearce ◽  
A. P. Torokhti

AbstractLet u be a random signal with realisations in an infinite-dimensional vector space X and υ an associated observable random signal with realisations in a finite-dimensional subspace Y ⊆ X. We seek a pointwise-best estimate of u using a bounded linear filter on the observed data vector υ. When x is a finite-dimensional Euclidean space and the covariance matrix for υ is nonsingular, it is known that the best estimate û of u is given by a standard matrix expression prescribing a linear mean-square filter. For the infinite-dimensional Hilbert space problem we show that the matrix expression must be replaced by an analogous but more general expression using bounded linear operators. The extension procedure depends directly on the theory of the Bochner integral and on the construction of appropriate HilbertSchmidt operators. An extended example is given.


Sign in / Sign up

Export Citation Format

Share Document