Pointwise absolutely convergent series of operators and related classes of Banach spaces

• Autorzy: Liudmyla Kadets , Vladimir Kadets
• Języki publikacji: EN

Abstrakty

EN

We study classes of operators represented as a pointwise absolutely convergent series of simpler ones, starting with rank 1 operators. In this short note we address the question, how far the repetition of this procedure can lead.

Słowa kluczowe

EN

Pointwise absolute convergence; Operator series; Dunford-Pettis operators

Kategorie tematyczne

• 30H05: Bounded analytic functions
• 46Bxx: Normed linear spaces and Banach spaces; Banach lattices
• 30Hxx: Spaces and algebras of analytic functions
• 40F05: Absolute and strong summability (should also be assigned at least one other classification number in Section 40)
• 40Fxx: Absolute and strong summability (should also be assigned at least one other classification number in Section 40)

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2012
• Tom: 10
• Numer: 2
• Strony: 603-608

Daty

wydano

2012-04-01

online

2012-01-18

Twórcy

autor

Liudmyla Kadets

• Kharkov V.N. Karazin National University

autor

Vladimir Kadets

• Kharkov V.N. Karazin National University

Bibliografia

• [1] Kadets V.M., A Course in Functional Analysis, Kharkov State University, Kharkov, 2006 (in Russian)
• [2] Kadets V., Kalton N., Werner D., Unconditionally convergent series of operators and narrow operators on L 1, Bull. London Math. Soc., 2005, 37(2), 265–274 http://dx.doi.org/10.1112/S0024609304003881
• [3] Lindenstrauss J., Tzafriri L., Classical Banach Spaces. I, Ergeb. Math. Grenzgeb., 92, Springer, Berlin-New York, 1977
• [4] Maslyuchenko O.V., Mykhaylyuk V.V., Popov M.M., A lattice approach to narrow operators, Positivity, 2009, 13(3), 459–495 http://dx.doi.org/10.1007/s11117-008-2193-z
• [5] Rosenthal H.P., Embeddings of L 1 in L 1, In: Conference in Modern Analysis and Probability, New Haven, June 8–11, 1982, Contemp. Math., 26, American Mathematical Society, Providence, 1984, 335–349

Identyfikatory

DOI

10.2478/s11533-011-0145-5