THE GELFAND–PHILLIPS AND DUNFORD–PETTIS TYPE PROPERTIES IN BIMODULES OF MEASURABLE OPERATORS
Huang J. Nessipbayev Y. Pliev M. Sukochev F.
September 2024American Mathematical Society
Transactions of the American Mathematical Society
2024#377Issue 96097 - 6149 pp.
We fully characterize noncommutative symmetric spaces E(M, τ) affiliated with a semifinite von Neumann algebra M equipped with a faithful normal semifinite trace τ on a (not necessarily separable) Hilbert space having the Gelfand–Phillips property and the WCG-property. The complete list of their relations with other classical structural properties (such as the Dunford–Pettis property, the Schur property and their variations) is given in the general setting of noncommutative symmetric spaces.
(weak/strong) Dunford–Pettis property , Gelfand–Phillips space , Noncommutative symmetric space , order continuous norm , WCG-space
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Institute for Advanced Study in Mathematics, HIT, Harbin, 150001, China
School of Mathematics and Statistics, University of New South Wales, Kensington, 2052, Australia
Institute of Mathematics and Mathematical Modeling, Almaty, 050010, Kazakhstan
Southern Mathematical Institute, The Russian Academy of Sciences, Vladikavkaz, 362027, Russian Federation
North Caucasus Center for Mathematical Research, The Vladikavkaz Scientific Center, the Russian Academy of Sciences, Vladikavkaz, 362027, Russian Federation
North-Ossetian State University, Vladikavkaz, 362025, Russian Federation
Institute for Advanced Study in Mathematics
School of Mathematics and Statistics
Institute of Mathematics and Mathematical Modeling
Southern Mathematical Institute
North Caucasus Center for Mathematical Research
North-Ossetian State University
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