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An example of a non-topologizable algebra

R. Frankiewicz, G. Plebanek (1995)

Studia Mathematica

We present an example of an algebra that is generated by ω 1 elements, and cannot be made a topological algebra. This answers a problem posed by W. Żelazko.

An example of a reflexive Lorentz Gamma space with trivial Boyd and Zippin indices

Alexei Karlovich, Eugene Shargorodsky (2021)

Czechoslovak Mathematical Journal

We show that for every p ( 1 , ) there exists a weight w such that the Lorentz Gamma space Γ p , w is reflexive, its lower Boyd and Zippin indices are equal to zero and its upper Boyd and Zippin indices are equal to one. As a consequence, the Hardy-Littlewood maximal operator is unbounded on the constructed reflexive space Γ p , w and on its associate space Γ p , w ' .

An explicit expression for the Kr functionals of interpolation between Lp spaces.

Jesús Bastero, Yves Raynaud, M. Luisa Rezola (1991)

Publicacions Matemàtiques

When dealing with interpolation spaces by real methods one is lead to compute (or at least to estimate) the K-functional associated to the couple of interpolation spaces. This concept was first introduced by J. Peetre (see [8], [9]) and some efforts have been done to find explicit expressions of it for the case of Lebesgue spaces. It is well known that for the couple consisting of L1 and L∞ on [0, ∞) K is given by K (t; f, L1, L∞) = ∫0t f* where f* denotes the non increasing rearrangement of the...

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