Difference between revisions of "Hille-Tamarkin operator"
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Let be an integral operator from
into
, i.e., there exists a
-measurable function
on
such that
a.e. on
. Then
is called a Hille–Tamarkin operator if
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where . By taking
one obtains the class of Hilbert–Schmidt operators (cf. Hilbert–Schmidt operator). Replacing
, respectively
, by arbitrary Banach function norms
, respectively
, one obtains the class of Hille–Tamarkin operators between Banach function spaces (sometimes called integral operators of finite double norm, see [a1]). Under some mild hypotheses on the norms, one can show that Hille–Tamarkin operators have rather strong compactness properties (see [a2]).
References
[a1] | A.C. Zaanen, "Riesz spaces" , II , North-Holland (1983) |
[a2] | A.R. Schep, "Compactness properties of Carleman and Hille–Tamarkin operators" Canad. J. Math. , 37 (1985) pp. 921–933 |
How to Cite This Entry:
Hille-Tamarkin operator. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Hille-Tamarkin_operator&oldid=22579
Hille-Tamarkin operator. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Hille-Tamarkin_operator&oldid=22579
This article was adapted from an original article by A.R. Schep (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article