Titlebook: Bounded Integral Operators on L 2 Spaces; Paul Richard Halmos,Viakalathur Shankar Sunder Book 1978 Springer-Verlag Berlin Heidelberg 1978

动物

Ferd Williams,B. Baron,S. P. Varmane that asks which operators . be integral operators (§16). The problem is one of recognition: if an integral operator on ..(.) is described in some manner other than by its kernel, how do its operatorial and measure-theoretic properties reflect the existence of a kernel that induces it? (Cf. Proble

Meager

Minatory

cutlery

Uniqueness, to ..(.). It is natural to ask: is that linear transformation injective? In other words: is an integral operator induced by only one kernel? The content of the following assertion is that the answer is yes.

PRE

Essential Spectrum,ty operator on ..(ℝ.) (which is not an integral operator) and the tensor product of the identity operator on ..(ℤ.) with a projection of rank 1 on ..(II) (which is an integral operator). What is the essential difference between these two kinds of examples?

diskitis

Characterization,ators? The question refers to unitary equivalence; in precise terms, it asks for a characterization of those operators . on ..(.) for which there exists a unitary operator . on ..(.) such that .* is integral.

表脸

Universality,ad of the existential one. In precise terms: under what conditions on an operator . on ..(.) does it happen that .* is an integral operator for every unitary . on ..(.)? When it does happen, the operator . will be called a . integral operator on ..(.).

舔食

Book 1978an integral operator is the natural "continuous" generali­ zation of the operators induced by matrices, and the only integrals that appear are the familiar Lebesgue-Stieltjes integrals on classical non-pathological mea­ sure spaces. The category. Some of the flavor of the theory can be perceived in

警告

analogous