A note on universal operators between separable Banach spaces

0525265 - MÚ 2021 RIV ES eng J - Journal Article
Garbulińska-Węgrzyn, J. - Kubiś, Wieslaw
A note on universal operators between separable Banach spaces.
Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Roč. 114, č. 3 (2020), č. článku 148. ISSN 1578-7303. E-ISSN 1579-1505
R&D Projects: GA ČR(CZ) GF20-22230L
Institutional support: RVO:67985840
Keywords : almost homogeneity * Gurariĭ property * Gurariĭ space * isometrically universal operator
OECD category: Pure mathematics
Impact factor: 2.169, year: 2020
Method of publishing: Open access
https://doi.org/10.1007/s13398-020-00878-4

We compare two types of universal operators constructed relatively recently by Cabello Sánchez, and the authors. The first operator Ω acts on the Gurariĭ space, while the second one PS has values in a fixed separable Banach space S. We show that if S is the Gurariĭ space, then both operators are isometric. We also prove that, for a fixed space S, the operator PS is isometrically unique. Finally, we show that Ω is generic in the sense of a natural infinite game.
Permanent Link: http://hdl.handle.net/11104/0309447