arXiv Analytics

Sign in

arXiv:0803.3646 [math.FA]AbstractReferencesReviewsResources

Characterizing Hilbert spaces using Fourier transform over the field of p-adic numbers

Yauhen Radyna, Yakov Radyno, Anna Sidorik

Published 2008-03-25Version 1

We characterize Hilbert spaces in the class of all Banach spaces using Fourier transform of vector-valued functions over the field $Q_p$ of $p$-adic numbers. Precisely, Banach space $X$ is isomorphic to a Hilbert one if and only if Fourier transform $F: L_2(Q_p,X)\to L_2(Q_p,X)$ in space of functions, which are square-integrable in Bochner sense and take value in $X$, is a bounded operator.

Comments: 6 pages, translation to English
Journal: Yauhen Radyna, Yakov Radyno, Anna Sidorik, Characterizing Hilbert spaces using Fourier transform over the field of p-adic numbers. Dokl. Nats. Akad. Nauk Belarusi, vol.51, No.5 (2007), p.17--22 (in russian)
Categories: math.FA
Subjects: 46C15, 43A25
Related articles: Most relevant | Search more
arXiv:math/0610421 [math.FA] (Published 2006-10-12)
Smooth norms and approximation in Banach spaces of the type C(K)
arXiv:math/9508207 [math.FA] (Published 1995-08-01)
Vector-valued Walsh-Paley martingales and geometry of Banach spaces
arXiv:math/0412171 [math.FA] (Published 2004-12-08)
Embedding $\ell_{\infty}$ into the space of all Operators on Certain Banach Spaces

Links

Toolbox