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Metric entropy of convex hulls in Hilbert spaces

Wenbo Li, Werner Linde (2000)

Studia Mathematica

Let T be a precompact subset of a Hilbert space. We estimate the metric entropy of co(T), the convex hull of T, by quantities originating in the theory of majorizing measures. In a similar way, estimates of the Gelfand width are provided. As an application we get upper bounds for the entropy of co(T), $T = t_{1}, t_{2}, . . .$ , $| | t_{j} | | \leq a_{j}$ , by functions of the $a_{j}$ ’s only. This partially answers a question raised by K. Ball and A. Pajor (cf. [1]). Our estimates turn out to be optimal in the case of slowly decreasing sequences ${(a_{j})}_{j = 1}^{\infty}$ .

M-Harmonic Besov p-spaces and Hankel operators in the Bergman Space on the Ball in Cn.

E.H. Youssfi, Kyong T. Hahn (1991)

Manuscripta mathematica

M-Ideals of Compact Operators.

Klaus Saatkamp (1978)

Mathematische Zeitschrift

Minimal projections onto spaces of symmetric matrices.

Mielczarek, Dominik (2006)

Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica

Minimal Reflexive Banach Lattices.

Heinrich P. Lotz (1974)

Mathematische Annalen

Minimalité de certains espaces fonctionnels et applications à la théorie des opérateurs

Y. Meyer (1984/1985)

Séminaire Équations aux dérivées partielles (Polytechnique)

Minimaxprinzipe zur Bestimmung der Eigenwerte J-nichtnegativer Operatoren.

Björn Textorius (1974)

Mathematica Scandinavica

Mittelergodische Halbgruppen linearer Operatoren

Rainer J. Nagel (1973)

Annales de l'institut Fourier

A semigroup $H$ in $L_{s} (E)$ , $E$ a Banach space, is called mean ergodic, if its closed convex hull in $L_{s} (E)$ has a zero element. Compact groups, compact abelian semigroups or contractive semigroups on Hilbert spaces are mean ergodic.Banach lattices prove to be a natural frame for further mean ergodic theorems: let $H$ be a bounded semigroup of positive operators on a Banach lattice $E$ with order continuous norm. $H$ is mean ergodic if there is a $H$ -subinvariant quasi-interior point of $E_{+}$ and a $H^{'}$ -subinvariant strictly...