Banach Journal of Mathematical Analysis

Traceability of positive integral operators in the absence of a metric

Valdir A. Menegatto, Ana P. Peron, and Mario H. de Castro

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We investigate the traceability of positive integral operators on $L^2(X,\mu)$ when $X$ is a Hausdorff locally compact second countable space and $\mu$ is a non-degenerate, $\sigma$-finite and locally finite Borel measure. This setting includes other cases proved in the literature, for instance the one in which $X$ is a compact metric space and $\mu$ is a special finite measure. The results apply to spheres, tori and other relevant subsets of the usual space $\mathbb{R}^m$.

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Banach J. Math. Anal., Volume 6, Number 2 (2012), 98-112.

First available in Project Euclid: 13 July 2012

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Zentralblatt MATH identifier

Primary: 47G10: Integral operators [See also 45P05]
Secondary: 47B34: Kernel operators 47B65: Positive operators and order-bounded operators 47B10: Operators belonging to operator ideals (nuclear, p-summing, in the Schatten-von Neumann classes, etc.) [See also 47L20] 42A82: Positive definite functions 60G46: Martingales and classical analysis

Integral operator positive definite kernel trace-class averaging martingale


de Castro, Mario H.; Menegatto, Valdir A.; Peron, Ana P. Traceability of positive integral operators in the absence of a metric. Banach J. Math. Anal. 6 (2012), no. 2, 98--112. doi:10.15352/bjma/1342210163.

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