Addendum to "Necessary condition for Kostyuchenko type systems to be a basis in Lebesgue spaces" (Colloq. Math. 127 (2012), 105-109)

• Autorzy: Aydin Sh. Shukurov
• Języki publikacji: EN

Abstrakty

EN

It is well known that if φ(t) ≡ t, then the system ${φⁿ(t)}_{n=0}^{∞}$ is not a Schauder basis in L₂[0,1]. It is natural to ask whether there is a function φ for which the power system ${φⁿ(t)}_{n=0}^{∞}$ is a basis in some Lebesgue space $L_{p}$. The aim of this short note is to show that the answer to this question is negative.

Kategorie tematyczne

• 46E30: Spaces of measurable functions ( L p -spaces, Orlicz spaces, K\"othe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
• 46B15: Summability and bases
• 46B25: Classical Banach spaces in the general theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2014
• Tom: 137
• Numer: 2
• Strony: 297-298

Daty

wydano

2014

Twórcy

autor

Aydin Sh. Shukurov

• Institute of Mathematics and Mechanics, NAS of Azerbaijan, Az1141, F. Agayev 9, Baku, Azerbaijan
• Baku State University, Baku, Azerbaijan

Identyfikatory

DOI

10.4064/cm137-2-12