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A note on \(\gamma\)-radonifying and summing operators. (English) Zbl 1334.60106

Chojnowska-Michalik, Anna (ed.) et al., Stochastic analysis. Special volume in honour of Jerzy Zabczyk. Selected papers based on the presentations at the Banach Center conference on stochastic analysis and control, Bȩdlewo, Poland, May 6–10, 2013. Warsaw: Polish Academy of Sciences, Institute of Mathematics (ISBN 978-83-86806-28-7/pbk). Banach Center Publications 105, 43-57 (2015).
Summary: In this note, we discuss certain generalizations of \(\gamma\)-radonifying operators and their applications to the regularity for linear stochastic evolution equations on some special Banach spaces. Furthermore, we also consider a more general class of operators, namely the so-called summing operators and discuss the application to the compactness of the heat semi-group between weighted \(L^{p}\)-spaces.
For the entire collection see [Zbl 1323.60004].

MSC:

60H15 Stochastic partial differential equations (aspects of stochastic analysis)
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
47B99 Special classes of linear operators
35R60 PDEs with randomness, stochastic partial differential equations
37H10 Generation, random and stochastic difference and differential equations
34F05 Ordinary differential equations and systems with randomness
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