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Some module cohomological properties of Banach algebras

Elham Ilka, Amin Mahmoodi, Abasalt Bodaghi (2020)

Mathematica Bohemica

We find some relations between module biprojectivity and module biflatness of Banach algebras 𝒜 and and their projective tensor product 𝒜 ^ . For some semigroups S , we study module biprojectivity and module biflatness of semigroup algebras l 1 ( S ) .

Some more weak Hubert spaces

Alec Edgington (1991)

Studia Mathematica

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.

Some new classes of topological vector spaces with closed graph theorems

Brian Rodrigues (1991)

Commentationes Mathematicae Universitatis Carolinae

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.

Some new inhomogeneous Triebel-Lizorkin spaces on metric measure spaces and their various characterizations

Dachun Yang (2005)

Studia Mathematica

Let ( X , ϱ , μ ) d , θ 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, | ϱ ( x , y ) - ϱ ( x ' , y ) | C ϱ ( x , x ' ) θ [ ϱ ( x , y ) + ϱ ( x ' , y ) ] 1 - θ , and μ is a nonnegative Borel regular measure on X such that for some d > 0 and all x ∈ X, μ ( y X : ϱ ( x , y ) < r ) r d . Let ε ∈ (0,θ], |s| < ε and maxd/(d+ε),d/(d+s+ε) < q ≤ ∞. The author introduces new inhomogeneous Triebel-Lizorkin spaces F q s ( X ) and establishes their frame characterizations by first establishing a Plancherel-Pólya-type inequality...

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