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2013•Bulletin of the Korean Mathematical SocietyOpen access

UNIFORMLY BOUNDED COMPOSITION OPERATORS ON A BANACH SPACE OF BOUNDED WIENER-YOUNG VARIATION FUNCTIONS

Dorota Głazowska, José Atilio Guerrero, Janusz Matkowski, Nelson Merentes

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Abstract

We prove, under some general assumptions, that a generator of any uniformly bounded Nemytskij operator, mapping a subset of space of functions of bounded variation in the sense of Wiener-Young into another space of this type, must be an affine function with respect to the second variable.

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We prove, under some general assumptions, that a generator of any uniformly bounded Nemytskij operator, mapping a subset of space of functions of bounded variation in the sense of Wiener-Young into another space of this type, must be an affine function with respect to the second variable.

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Available abstract

We prove, under some general assumptions, that a generator of any uniformly bounded Nemytskij operator, mapping a subset of space of functions of bounded variation in the sense of Wiener-Young into another space of this type, must be an affine function with respect to the second variable.

Key concepts: Mathematics, Bounded function, Bounded operator, Bounded inverse theorem, Bounded variation, Banach space, Operator space, Pure mathematics

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