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Direct limit of matricially Riesz normed spaces

J. V. Ramani, Anil Kumar Karn, Sunil Yadav (2006)

Commentationes Mathematicae Universitatis Carolinae

In this paper, the -Riesz norm for ordered -bimodules is introduced and characterized in terms of order theoretic and geometric concepts. Using this notion, -Riesz normed bimodules are introduced and characterized as the inductive limits of matricially Riesz normed spaces.

Direct limit of matrix order unit spaces

J. V. Ramani, Anil K. Karn, Sunil Yadav (2008)

Colloquium Mathematicae

The notion of ℱ-approximate order unit norm for ordered ℱ-bimodules is introduced and characterized in terms of order-theoretic and geometric concepts. Using this notion, we characterize the inductive limit of matrix order unit spaces.

Directional moduli of rotundity and smoothness

Michael O. Bartlett, John R. Giles, Jon D. Vanderwerff (1999)

Commentationes Mathematicae Universitatis Carolinae

We study various notions of directional moduli of rotundity and when such moduli of rotundity of power type imply the underlying space is superreflexive. Duality with directional moduli of smoothness and some applications are also discussed.

Directionally Euclidean structures of Banach spaces

Jarno Talponen (2011)

Studia Mathematica

We study Banach spaces with directionally asymptotically controlled ellipsoid-approximations of the unit ball in finite-dimensional sections. Here these ellipsoids are the unique minimum volume ellipsoids, which contain the unit ball of the corresponding finite-dimensional subspace. The directional control here means that we evaluate the ellipsoids by means of a given functional of the dual space. The term 'asymptotical' refers to the fact that we take 'lim sup' over finite-dimensional subspaces. ...

Dirichlet series induced by the Riemann zeta-function

Jun-ichi Tanaka (2008)

Studia Mathematica

The Riemann zeta-function ζ(s) extends to an outer function in ergodic Hardy spaces on ω , the infinite-dimensional torus indexed by primes p. This enables us to investigate collectively certain properties of Dirichlet series of the form ( a p , s ) = p ( 1 - a p p - s ) - 1 for a p in ω . Among other things, using the Haar measure on ω for measuring the asymptotic behavior of ζ(s) in the critical strip, we shall prove, in a weak sense, the mean-value theorem for ζ(s), equivalent to the Lindelöf hypothesis.

Discontinuity of the product in multiplier algebras.

Mohamed Oudadess (1990)

Publicacions Matemàtiques

Entire functions operate in complete locally A-convex algebras but not continuously. Actually squaring is not always continuous. The counterexample we give is multiplier algebra.

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