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Hermitian powers: A Müntz theorem and extremal algebras

M. J. Crabb, J. Duncan, C. M. McGregor, T. J. Ransford (2001)

Studia Mathematica

Given ⊂ ℕ, let ̂ be the set of all positive integers m for which h m is hermitian whenever h is an element of a complex unital Banach algebra A with hⁿ hermitian for each n ∈ . We attempt to characterize when (i) ̂ = ℕ, or (ii) ̂ = . A key tool is a Müntz-type theorem which gives remarkable conclusions when 1 ∈ and ∑ 1/n: n ∈ diverges. The set ̂ is determined by a single extremal Banach algebra Ea(). We describe this extremal algebra for various .

Herz-Type Hardy Spaces for the Dunkl Operator on the Real Line

Gasmi, A., Sifi, M., Soltani, F. (2006)

Fractional Calculus and Applied Analysis

2000 Mathematics Subject Classification: Primary 46F12, Secondary 44A15, 44A35We introduce some new weighted Herz spaces associated with the Dunkl operator on R. Also we characterize by atomic decompositions the corresponding Herz-type Hardy spaces. As applications we investigate the Dunkl transform on these spaces and establish a version of Hardy inequality for this transform.* The authors are supported by the DGRST research project 04/UR/15-02.

Hessian determinants as elements of dual Sobolev spaces

Teresa Radice (2014)

Studia Mathematica

In this short note we present new integral formulas for the Hessian determinant. We use them for new definitions of Hessian under minimal regularity assumptions. The Hessian becomes a continuous linear functional on a Sobolev space.

High order representation formulas and embedding theorems on stratified groups and generalizations

Guozhen Lu, Richard Wheeden (2000)

Studia Mathematica

We derive various integral representation formulas for a function minus a polynomial in terms of vector field gradients of the function of appropriately high order. Our results hold in the general setting of metric spaces, including those associated with Carnot-Carathéodory vector fields, under the assumption that a suitable L 1 to L 1 Poincaré inequality holds. Of particular interest are the representation formulas in Euclidean space and stratified groups, where polynomials exist and L 1 to L 1 Poincaré...

Higher order spreading models

S. A. Argyros, V. Kanellopoulos, K. Tyros (2013)

Fundamenta Mathematicae

We introduce higher order spreading models associated to a Banach space X. Their definition is based on ℱ-sequences ( x s ) s ∈ ℱ with ℱ a regular thin family and on plegma families. We show that the higher order spreading models of a Banach space X form an increasing transfinite hierarchy ( ℳ ξ ( X ) ) ξ < ω ₁ . Each ℳ ξ ( X ) contains all spreading models generated by ℱ-sequences ( x s ) s ∈ ℱ with order of ℱ equal to ξ. We also study the fundamental properties of this hierarchy.

Higher-dimensional weak amenability

B. Johnson (1997)

Studia Mathematica

Bade, Curtis and Dales have introduced the idea of weak amenability. A commutative Banach algebra A is weakly amenable if there are no non-zero continuous derivations from A to A*. We extend this by defining an alternating n-derivation to be an alternating n-linear map from A to A* which is a derivation in each of its variables. Then we say that A is n-dimensionally weakly amenable if there are no non-zero continuous alternating n-derivations on A. Alternating n-derivations are the same as alternating...

Higher-Order Partial Differentiation

Noboru Endou, Hiroyuki Okazaki, Yasunari Shidama (2012)

Formalized Mathematics

In this article, we shall extend the formalization of [10] to discuss higher-order partial differentiation of real valued functions. The linearity of this operator is also proved (refer to [10], [12] and [13] for partial differentiation).

Hilbert C*-modules and amenable actions

Ronald G. Douglas, Piotr W. Nowak (2010)

Studia Mathematica

We study actions of discrete groups on Hilbert C*-modules induced from topological actions on compact Hausdorff spaces. We show non-amenability of actions of non-amenable and non-a-T-menable groups, provided there exists a quasi-invariant probability measure which is sufficiently close to being invariant.

Hilbert C*-modules from group actions: beyond the finite orbits case

Michael Frank, Vladimir Manuilov, Evgenij Troitsky (2010)

Studia Mathematica

Continuous actions of topological groups on compact Hausdorff spaces X are investigated which induce almost periodic functions in the corresponding commutative C*-algebra. The unique invariant mean on the group resulting from averaging allows one to derive a C*-valued inner product and a Hilbert C*-module which serve as an environment to describe characteristics of the group action. For Lyapunov stable actions the derived invariant mean M ( ϕ x ) is continuous on X for any ϕ ∈ C(X), and the induced C*-valued...

Hilbert modules and tensor products of operator spaces

Bojan Magajna (1997)

Banach Center Publications

The classical identification of the predual of B(H) (the algebra of all bounded operators on a Hilbert space H) with the projective operator space tensor product H ¯ ⨂ ^ H is extended to the context of Hilbert modules over commutative von Neumann algebras. Each bounded module homomorphism b between Hilbert modules over a general C*-algebra is shown to be completely bounded with ∥ b ∥ c b = ∥ b ∥ . The so called projective operator tensor product of two operator modules X and Y over an abelian von Neumann algebra C is introduced...

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