Operators with large diagonal

Beschreibung

Given a Banach space X with an unconditional basis, we consider the following question: does the identity on X factor through every bounded operator on X with large diagonal relative to the unconditional basis? We show that on Gowers’ space with its unconditional basis there exists an operator for which the answer to the question is negative. By contrast, for any operator on the mixed-norm Hardy spaces Hp(Hq), where 1 <= p, q < \infty, with the bi-parameter Haar system, this problem always has a positive solution. The one-parameter Hp spaces were treated first by Andrew [1] in 1979.

Zeitraum	15 Okt. 2015
Ereignistitel	unbekannt/unknown
Veranstaltungstyp	Sonstiges
Ort	PolenAuf Karte anzeigen