• Corpus ID: 18229032

Topological vector spaces

  title={Topological vector spaces},
  author={Paul B. Garrett},
ing the above, for a (not necessarily countable) family . . . φ2 // B1 φ1 // Bo of Banach spaces with continuous linear transition maps as indicated, not recessarily requiring the continuous linear maps to be injective (or surjective), a (projective) limit limiBi is a topological vector space with continuous linear maps limiBi → Bj such that, for every compatible family of continuous linear maps Z → Bi there is unique continuous linear Z → limiBi fitting into limiBi !! . . . φ2 // B1 φ1 // Bo Z… 

Linearly continuous functions and F (cid:2) -measurability

The linear continuity of a function defined on a vector space means that its restriction to every affine line is continuous. For functions defined on R m this notion is close to the separate continuity

On integration in banach spaces and total sets

Abstract Let X be a Banach space and Γ ⊆ X∗ a total linear subspace. We study the concept of Γ-integrability for X-valued functions f defined on a complete probability space, i.e. an analogue of

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Cembranos and Freniche proved that for every two infinite compact Hausdorff spaces X and Y the Banach space C ( X × Y ) of continuous real-valued functions on X × Y endowed with the supremum norm

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. Denote by K n 0 the family of all closed convex sets A ⊂ R n containing the origin 0 ∈ R n . For A ∈ K n 0 , its polar set is denoted by A ◦ . In this paper, we investigate the topological nature

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Let E, F be two topological spaces and u : E → F be a map. If F is Haudorff and u is continuous, then its graph is closed. The Closed Graph Theorem establishes the converse when E and F are suitable

On the theory of balayage on locally compact spaces

  • N. Zorii
  • Mathematics
    Potential Analysis
  • 2022
The paper deals with the theory of balayage of Radon measures μ of finite energy on a locally compact space X with respect to a consistent kernel κ satisfying the domination principle. Such theory is

On Ranges of Non-linear Operators

We derive conditions ensuring that the range of a given continuous mapping with a compact convex domain covers a prescribed set. In Fréchet spaces, we consider approximations by one single-valued

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  • K. Keimel
  • Mathematics
    Log. Methods Comput. Sci.
  • 2015
A conceptual approach inspired by classical functional analysis is presented, presenting a conceptual approach to functional analysis which may prove useful in other situations.