Some linear topological properties of the hardy spaces
We find some relations between module biprojectivity and module biflatness of Banach algebras and and their projective tensor product . For some semigroups , we study module biprojectivity and module biflatness of semigroup algebras .
We construct, by a variation of the method used to construct the Tsirelson spaces, a new family of weak Hilbert spaces which contain copies of l₂ inside every subspace.
In this note, we investigate non-locally-convex topological vector spaces for which the closed graph theorem holds. In doing so, we introduce new classes of topological vector spaces. Our study includes a direct extension of Pták duality to the non-locally-convex situation.
Let be a space of homogeneous type, i.e. X is a set, ϱ is a quasi-metric on X with the property that there are constants θ ∈ (0,1] and C₀ > 0 such that for all x,x’,y ∈ X, , and μ is a nonnegative Borel regular measure on X such that for some d > 0 and all x ∈ X, . Let ε ∈ (0,θ], |s| < ε and maxd/(d+ε),d/(d+s+ε) < q ≤ ∞. The author introduces new inhomogeneous Triebel-Lizorkin spaces and establishes their frame characterizations by first establishing a Plancherel-Pólya-type inequality...