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A Borel extension approach to weakly compact operators on C 0 ( T )

Thiruvaiyaru V. Panchapagesan (2002)

Czechoslovak Mathematical Journal

Let X be a quasicomplete locally convex Hausdorff space. Let T be a locally compact Hausdorff space and let C 0 ( T ) = { f T I , f is continuous and vanishes at infinity } be endowed with the supremum norm. Starting with the Borel extension theorem for X -valued σ -additive Baire measures on T , an alternative proof is given to obtain all the characterizations given in [13] for a continuous linear map u C 0 ( T ) X to be weakly compact.

A class of pairs of weights related to the boundedness of the Fractional Integral Operator between L p and Lipschitz spaces

Gladis Pradolini (2001)

Commentationes Mathematicae Universitatis Carolinae

In [P] we characterize the pairs of weights for which the fractional integral operator I γ of order γ from a weighted Lebesgue space into a suitable weighted B M O and Lipschitz integral space is bounded. In this paper we consider other weighted Lipschitz integral spaces that contain those defined in [P], and we obtain results on pairs of weights related to the boundedness of I γ acting from weighted Lebesgue spaces into these spaces. Also, we study the properties of those classes of weights and compare...

A counterexample in operator theory

Antonio Córdoba (1993)

Publicacions Matemàtiques

The purpose of this note is to give an explicit construction of a bounded operator T acting on the space L2[0,1] such that |Tf(x)| ≤ ∫01 |f(y)| dy for a.e. x ∈ [0.1], and, nevertheless, ||T||Sp = ∞ for every p < 2. Here || ||Sp denotes the norm associated to the Schatten-Von Neumann classes.

A note on Howe's oscillator semigroup

Joachim Hilgert (1989)

Annales de l'institut Fourier

Analytic extensions of the metaplectic representation by integral operators of Gaussian type have been calculated in the L 2 ( n ) and the Bargmann-Fock realisations by Howe [How2] and Brunet-Kramer [Brunet-Kramer, Reports on Math. Phys., 17 (1980), 205-215]], respectively. In this paper we show that the resulting semigroups of operators are isomorphic and calculate the intertwining operator.

A note on Markov operators and transition systems

Bartosz Frej (2002)

Colloquium Mathematicae

On a compact metric space X one defines a transition system to be a lower semicontinuous map X 2 X . It is known that every Markov operator on C(X) induces a transition system on X and that commuting of Markov operators implies commuting of the induced transition systems. We show that even in finite spaces a pair of commuting transition systems may not be induced by commuting Markov operators. The existence of trajectories for a pair of transition systems or Markov operators is also investigated.

A note on the convolution theorem for the Fourier transform

Charles S. Kahane (2011)

Czechoslovak Mathematical Journal

In this paper we characterize those bounded linear transformations T f carrying L 1 ( 1 ) into the space of bounded continuous functions on 1 , for which the convolution identity T ( f * g ) = T f · T g holds. It is shown that such a transformation is just the Fourier transform combined with an appropriate change of variable.

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