On products of noncommutative symmetric quasi Banach spaces and applications
Bekjan T.N. Ospanov M.N.
February 2021Birkhauser
Positivity
2021#25Issue 1121 - 148 pp.
Let E1,E2 be symmetric quasi Banach function spaces on (0,α)(0<α≤∞). We study some properties of several constructions (the products E1(M) ⊙ E2(M) , the Calderón spaces E1(M) θE2(M) 1-θ, the complex interpolation spaces (E1(M),E2(M))θ, the real interpolation method (E1(M),E2(M))θ,p) in the context of noncommutative symmetric quasi Banach spaces. Under some natural assumptions, we prove (E1(M),E2(M))θ=E1(M)θE2(M)1-θ=E1(1θ)(M)⊙E2(11-θ)(M)(0<θ<1).As application, we extend these result to the noncommutative symmetric quasi Hardy spaces case. We also obtained the real case of Peter Jones’ theorem for noncommutative symmetric quasi Hardy spaces.
Complex and real interpolation , Noncommutative symmetric quasi Banach space , Noncommutative symmetric quasi Hardy space , Pointwise product of symmetric quasi Banach function spaces , Symmetric quasi Banach function space
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College of Mathematics and Systems Science, Xinjiang University, Ürümqi, 830046, China
Faculty of Mechanics and Mathematics, L. N. Gumilyov Eurasian National University, Nur-Sultan, 010008, Kazakhstan
College of Mathematics and Systems Science
Faculty of Mechanics and Mathematics
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