‎it is well known that every (real or complex) normed linear space $l$ is isometrically embeddable into $c(x)$ for some compact hausdorff space $x$‎. ‎here $x$ is the closed unit ball of $l^*$ (the set of all continuous scalar-valued linear mappings on $l$) endowed with the weak$^*$ topology‎, ‎which is compact by the banach--alaoglu theorem‎. ‎we prove that the compact hausdorff space $x$ can ...

The aim of the present paper is to introduce the asymmetric locally convex spaces and to prove some basic properties. Among these I do mention the analogs of the EidelheitTuckey separation theorems, of the Alaoglu-Bourbaki theorem on the weak compactness of the polar of a neighborhood of 0, and a Krein-Milman-type theorem. These results extend those obtained by Garcı́a-Raffi et al. (2003) and Co...

We initiate a study of cohomological aspects of weakly almost periodic group representations on Banach spaces, in particular, isometric representations on reflexive Banach spaces. Using the Ryll-Nardzewski fixed point Theorem, we prove a vanishing result for the restriction map (with respect to a subgroup) in the reduced cohomology of weakly periodic representations. Combined with the Alaoglu-B...

We give a domain-theoretic analogue of the classical BanachAlaoglu theorem, showing that the patch topology on the weak* topology is compact. Various theorems follow concerning the stable compactness of spaces of valuations on a topological space. We conclude with reformulations of the patch topology in terms of polar sets or Minkowski functionals, showing, in particular, that the ‘sandwich set...

We describe an implementation of a pointfree proof of the Alaoglu and the Hahn-Banach theorems in Type Theory. The proofs described here are formalisations of the proofs presented in \The Hahn-Banach Theorem in Type Theory" 4]. The implementation was partially developed simultaneously with 4] and it was a help in the development of the informal proofs.

Introduction. The question of ergodicity of a semigroup of bounded linear operators on a Banach space has been reduced, by Alaoglu and Birkhoff [l],1 Day [2, 3], and Eberlein [4], to the study firstly of the ergodicity of the semigroup itself and secondly, of the ergodicity of each element of the Banach space with respect to this ergodic semigroup. In the case of a bounded and commutative semig...

The paper is concerned with compact bilinear operators on asymmetric normed spaces. study of multilinear spaces was initiated by Latreche and Dahia (2020) [24]. We go further in this direction prove a Schauder type theorem the compactness adjoint operator ideal properties operators. These extend some results Ramanujan Schock (1985) [34], Ruch (1989) [36], Banach On space forms one introduces an...

The classical Hahn-Banach Theorem states that any linear bounded functional defined on a linear subspace of a normed space admits a norm-preserving linear bounded extension to the whole space. The constructive and computational content of this theorem has been studied by Bishop, Bridges, Metakides, Nerode, Shore, Kalantari, Downey, Ishihara and others and it is known that the theorem does not a...