On quasi-compactness of operator nets on Banach spaces

• Autorzy: Eduard Yu. Emel'yanov
• Języki publikacji: EN

Abstrakty

EN

The paper introduces a notion of quasi-compact operator net on a Banach space. It is proved that quasi-compactness of a uniform Lotz-Räbiger net $(T_{λ})_{λ}$ is equivalent to quasi-compactness of some operator $T_{λ}$. We prove that strong convergence of a quasi-compact uniform Lotz-Räbiger net implies uniform convergence to a finite-rank projection. Precompactness of operator nets is also investigated.

Kategorie tematyczne

• 47S99: None of the above, but in this section
• 47A35: Ergodic theory
• 47B99: None of the above, but in this section
• 47L05: Linear spaces of operators

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2011
• Tom: 203
• Numer: 2
• Strony: 163-170

Daty

wydano

2011

Twórcy

autor

Eduard Yu. Emel'yanov

• Department of Mathematics, Middle East Technical University, 06531 Ankara, Turkey
• Sobolev Institute of Mathematics, 630090 Novosibirsk, Russia

Identyfikatory

DOI

10.4064/sm203-2-3