Narrow operators (a survey)

• Autorzy: Mikhail Popov
• Języki publikacji: EN

Abstrakty

EN

Narrow operators are those operators defined on function spaces which are "small" at signs, i.e., at {-1,0,1}-valued functions. We summarize here some results and problems on them. One of the most interesting things is that if E has an unconditional basis then each operator on E is a sum of two narrow operators, while the sum of two narrow operators on L₁ is narrow. Recently this notion was generalized to vector lattices. This generalization explained the phenomena of sums: the set of all regular narrow operators is a band in the vector lattice of all regular operators (in particular, a subspace). In L₁ all operators are regular, and in spaces with unconditional bases narrow operators with non-narrow sum are non-regular. Nevertheless, a new lattice approach has led to new interesting problems.

Kategorie tematyczne

• 46B20: Geometry and structure of normed linear spaces
• 46B10: Duality and reflexivity
• 46B03: Isomorphic theory (including renorming) of Banach spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2011
• Tom: 92
• Numer: 1
• Strony: 299-326

Daty

wydano

2011

Twórcy

autor

Mikhail Popov

• Department of Applied Mathematics, Chernivtsi National University str. Kotsiubyns'koho 2, Chernivtsi, 58012 Ukraine

Identyfikatory

DOI

10.4064/bc92-0-21