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Speaker: Nikolay Zhuravlev, PhD.

Topic: The fundamental theorem of calculus for Banach space-valued functions

Annotation. We prove the commutation of the Bochner integral with multiplication (in the sense of composition) by a bounded operator. As an application of this property, we show how the fundamental theorem of calculus for Banach space-valued functions follows from a similar theorem in the scalar case. We will also construct a total set in the corresponding L_2 function space with values in the Hilbert space.