SUBSYMMETRIC LINEAR CONTINUOUS FUNCTIONALS ON SPACES OF LEBESGUE INTEGRABLE FUNCTIONS ON THE SEMI-AXIS

Authors

  • I.Ya. Ivasyuk Vasyl Stefanyk Carpathian National University, Ivano-Frankivsk, Ukraine
  • S.I. Nykorovych Vasyl Stefanyk Carpathian National University, Ivano-Frankivsk, Ukraine
  • A.V. Solomko Vasyl Stefanyk Carpathian National University, Ivano-Frankivsk, Ukraine

DOI:

https://doi.org/10.31471/2304-7399-2025-21(79)-52-58

Keywords:

linear functional, subsymmetric function, Banach space, Lebesgue integrable function

Abstract

The work is devoted to the study of subsymmetric continuous linear functionals on real and complex topological vector spaces of Lebesgue integrable functions on the semi-axis. We consider the class of such spaces satisfying some natural conditions. The complete description of the structure of a subsymmetric continuous linear functional defined on an arbitrary representative of this class has been found.
Specifically, we show that every such a functional can be represented as an integral of its argument up to multiplication by a constant.

References

1. Bihun V., Dolishniak D., Kravtsiv V., Zagorodnuyk A. Subsymmetric polynomials on Banach spaces and their applications, Mathematics, 13 (2025), no. 22, Article number 3693. https://doi.org/10.3390/math13223693

2. Gonzalo R. Multilinear forms, subsymmetric polynomials, and spreading models on Banach spaces, JMAA, 202 (1996), no. 2, 379–

397. https://doi.org/10.1006/jmaa.1996.0322

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Published

2025-12-09

How to Cite

Ivasyuk, I., Nykorovych, S., & Solomko, A. (2025). SUBSYMMETRIC LINEAR CONTINUOUS FUNCTIONALS ON SPACES OF LEBESGUE INTEGRABLE FUNCTIONS ON THE SEMI-AXIS. PRECARPATHIAN BULLETIN OF THE SHEVCHENKO SCIENTIFIC SOCIETY. Number, (21(79), 52–58. https://doi.org/10.31471/2304-7399-2025-21(79)-52-58

Issue

No. 21(79) (2025): PRECARPATHIAN BULLETIN OF THE SHEVCHENKO SCIENTIFIC SOCIETY Number

Section

Mathematics and Mechanics