Hilbert Space Problem Four

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

A Hilbert Space Problem Book. By Paul R. Haimos

1984 ◽  
Vol 91 (9) ◽  
pp. 592-594
Author(s):  
Peter Fillmore ◽  
Nigel Higson
Keyword(s):  
Hilbert Space ◽  
Space Problem ◽  
Problem Book

A Hilbert Space Problem Book

1989 ◽  
Vol 73 (465) ◽  
pp. 259
Author(s):  
Philip Maher ◽  
P. R. Halmos
Keyword(s):  
Hilbert Space ◽  
Space Problem ◽  
Problem Book

Hilbert Space Problem Four

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

A contribution to the solution of the compact correction problem for operators on a Banach space

1989 ◽  
Vol 31 (2) ◽  
pp. 219-229
Author(s):  
Mícheál Ó Searcóid
Keyword(s):  
Banach Space ◽  
Hilbert Space ◽  
Compact Operator ◽  
Complex Number ◽  
Space Problem ◽  
Riesz Operators ◽  
Correction Problem ◽  
Bounded Below ◽  
General Banach Space

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.

A HILBERT SPACE PROBLEM BOOK

1968 ◽  
Vol s1-43 (1) ◽  
pp. 565-565
Author(s):  
F. Smithies
Keyword(s):  
Hilbert Space ◽  
Space Problem ◽  
Problem Book

A Hilbert Space Problem Book.

1984 ◽  
Vol 91 (9) ◽  
pp. 592
Author(s):  
Peter Fillmore ◽  
Nigel Higson ◽  
Paul R. Halmos
Keyword(s):  
Hilbert Space ◽  
Space Problem ◽  
Problem Book

scholarly journals An optimal linear filter for random signals with realisations in a separable Hilbert space

2003 ◽  
Vol 44 (4) ◽  
pp. 485-500 ◽  
Author(s):  
P. G. Howlett ◽  
C. E. M. Pearce ◽  
A. P. Torokhti
Keyword(s):  
Hilbert Space ◽  
Random Signal ◽  
Finite Dimensional Subspace ◽  
Linear Filter ◽  
Bounded Linear ◽  
Space Problem ◽  
Infinite Dimensional ◽  
Finite Dimensional ◽  
Best Estimate ◽  
Matrix Expression

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.

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