Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 44, 2019, 945-964

LINEAR AND CONTINUOUS OPERATORS ON KÖTHE–BOCHNER SPACES

Ion Chiţescu and Răzvan-Cornel Sfetcu

University of Bucharest, Faculty of Mathematics and Computer Science
Str. Academiei 14, 010014, Bucharest, Romania
University Politehnica of Bucharest
Str. Splaiul Independenţei 313, 060042, Bucharest, Romania; ionchitescu 'at' yahoo.com

University of Bucharest, Faculty of Mathematics and Computer Science
Str. Academiei 14, 010014, Bucharest, Romania; razvancornelsfetcu 'at' gmail.com

Abstract. The Köthe–Bochner spaces L_ρ(E) are the vector valued version of the scalar Köthe spaces L_ρ, which generalize the Lebesgue spaces L^p, the Orlicz spaces and many other functional spaces. In the present paper we study the linear and continuous operators U : L_ρ(E) → F, giving integral representations for them. These operators generate operators V : L_ρ → L(E,F) which we call "natural operators" and study here.

2010 Mathematics Subject Classification: Primary 46E30, 46E40, 47B38, 47G10; Secondary 28A20, 54A20, 54C35, 54E25.

Key words: Köthe space, Köthe–Bochner space, linear and continuous operator, variation of a measure, semivariation of a measure.

Reference to this article: I. Chiţescu and R.-C. Sfetcu: Linear and continuous operators on Köthe–Bochner spaces. Ann. Acad. Sci. Fenn. Math. 44 (2019), 945-964.

Full document as PDF file

https://doi.org/10.5186/aasfm.2019.4454