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Minimal projections with respect to various norms

Asuman Güven Aksoy, Grzegorz Lewicki (2012)

Studia Mathematica

A theorem of Rudin permits us to determine minimal projections not only with respect to the operator norm but with respect to various norms on operator ideals and with respect to numerical radius. We prove a general result about N-minimal projections where N is a convex and lower semicontinuous (with respect to the strong operator topology) function and give specific examples for the cases of norms or seminorms of p-summing, p-integral and p-nuclear operator ideals.

Minimax theorems without changeless proportion

Liang-Ju Chu, Chi-Nan Tsai (2003)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

The so-called minimax theorem means that if X and Y are two sets, and f and g are two real-valued functions defined on X×Y, then under some conditions the following inequality holds: i n f y ∈ Y s u p x ∈ X f ( x , y ) ≤ s u p x ∈ X i n f y ∈ Y g ( x , y ) . We will extend the two functions version of minimax theorems without the usual condition: f ≤ g. We replace it by a milder condition: s u p x ∈ X f ( x , y ) ≤ s u p x ∈ X g ( x , y ) , ∀y ∈ Y. However, we require some restrictions; such as, the functions f and g are jointly upward, and their upper sets are connected. On the other hand, by using some properties...

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...

Mixed-type reverse order law and its equivalents

Nebojša Č. Dinčić, Dragan S. Djordjević, Dijana Mosić (2011)

Studia Mathematica

We present new results related to various equivalents of the mixed-type reverse order law for the Moore-Penrose inverse for operators on Hilbert spaces. Recent finite-dimensional results of Tian are extended to Hilbert space operators.

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