On Arens-Michael algebras which do not have non-zero injective ⨶-modules

A. Pirkovskii

Displaying similar documents to “On Arens-Michael algebras which do not have non-zero injective ⨶-modules”

Representations of the spaces $C^{\infty} (ℝ^{N}) \cap H^{k, p} (ℝ^{N})$

A. Albanese, V. Moscatelli (2000)

Studia Mathematica

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We give a representation of the spaces $C^{\infty} (ℝ^{N}) \cap H^{k, p} (ℝ^{N})$ as spaces of vector-valued sequences and use it to investigate their topological properties and isomorphic classification. In particular, it is proved that $C^{\infty} (ℝ^{N}) \cap H^{k, 2} (ℝ^{N})$ is isomorphic to the sequence space $s^{ℕ} \cap l^{2} (l^{2})$ , thereby showing that the isomorphy class does not depend on the dimension N if p=2.

Uniqueness of complete norms for quotients of Banach function algebras

W. Bade, H. Dales (1993)

Studia Mathematica

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We prove that every quotient algebra of a unital Banach function algebra A has a unique complete norm if A is a Ditkin algebra. The theorem applies, for example, to the algebra A (Γ) of Fourier transforms of the group algebra $L^{1} (G)$ of a locally compact abelian group (with identity adjoined if Γ is not compact). In such algebras non-semisimple quotients $A (Γ) / \bar{J (E)}$ arise from closed subsets E of Γ which are sets of non-synthesis. Examples are given to show that the condition of Ditkin cannot be relaxed....

A new Taylor type formula and $C^{\infty}$ extensions for asymptotically developable functions

M. Zurro (1997)

Studia Mathematica

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The paper studies the relation between asymptotically developable functions in several complex variables and their extensions as functions of real variables. A new Taylor type formula with integral remainder in several variables is an essential tool. We prove that strongly asymptotically developable functions defined on polysectors have $C^{\infty}$ extensions from any subpolysector; the Gevrey case is included.

Holomorphic motions commuting with semigroups

Zbigniew Słodkowski (1996)

Studia Mathematica

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A holomorphic family $f_{z}$ , |z|<1, of injections of a compact set E into the Riemann sphere can be extended to a holomorphic family of homeomorphisms $F_{z}$ , |z|<1, of the Riemann sphere. (An earlier result of the author.) It is shown below that there exist extensions $F_{z}$ which, in addition, commute with some holomorphic families of holomorphic endomorphisms of $ℂ ̅ ̅ ̅ ̅ ̅ ̅ f_{z} (E)$ , |z|<1 (under suitable assumptions). The classes of covering maps and maps with the path lifting property are discussed. ...

$B M O_{ψ}$ -spaces and applications to extrapolation theory

Stefan Geiss (1997)

Studia Mathematica

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We investigate a scale of $B M O_{ψ}$ -spaces defined with the help of certain Lorentz norms. The results are applied to extrapolation techniques concerning operators defined on adapted sequences. Our extrapolation works simultaneously with two operators, starts with $B M O_{ψ}$ - $L_{\infty}$ -estimates, and arrives at $L_{p}$ - $L_{p}$ -estimates, or more generally, at estimates between K-functionals from interpolation theory.

Montel and reflexive preduals of spaces of holomorphic functions on Fréchet spaces

Christopher Boyd (1993)

Studia Mathematica

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For U open in a locally convex space E it is shown in [31] that there is a complete locally convex space G(U) such that $G {(U)}_{i}^{'} = (ℋ (U), τ_{δ})$ . Here, we assume U is balanced open in a Fréchet space and give necessary and sufficient conditions for G(U) to be Montel and reflexive. These results give an insight into the relationship between the $τ_{0}$ and $τ_{ω}$ topologies on ℋ (U).

Every separable Banach space has a bounded strong norming biorthogonal sequence which is also a Steinitz basis

Paolo Terenzi (1994)

Studia Mathematica

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Every separable, infinite-dimensional Banach space X has a biorthogonal sequence $z_{n}, z *_{n}$ , with $s p a n z *_{n}$ norming on X and $∥ z_{n} ∥ + ∥ z *_{n} ∥$ bounded, so that, for every x in X and x* in X*, there exists a permutation π(n) of n so that $x \in \bar{c o n v} f i n i t e s u b s e r i e s o f \sum_{n = 1}^{\infty} z *_{n} (x) z_{n} a n d x *_{n} (x) = \sum_{n = 1}^{\infty} z *_{π (n)} (x) x * (z_{π (n)})$ .

$L^{p}$ -improving properties of measures supported on curves on the Heisenberg group

Silvia Secco (1999)

Studia Mathematica

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$L^{p}$ - $L^{q}$ boundedness properties are obtained for operators defined by convolution with measures supported on certain curves on the Heisenberg group. We find the curvature condition for which the type set of these operators can be the full optimal trapezoid with vertices A=(0,0), B=(1,1), C=(2/3,1/2), D=(1/2,1/3). We also give notions of right curvature and left curvature which are not mutually equivalent.

A characterization of some weighted norm inequalities for the fractional maximal function

Richard Wheeden (1993)

Studia Mathematica

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A new characterization is given for the pairs of weight functions v, w for which the fractional maximal function is a bounded operator from $L_{v}^{p} (X)$ to $L_{w}^{q} (X)$ when 1 < p < q < ∞ and X is a homogeneous space with a group structure. The case when X is n-dimensional Euclidean space is included.

Mixed-norm spaces and interpolation

Joaquín Ortega, Joan Fàbrega (1994)

Studia Mathematica

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Let D be a bounded strictly pseudoconvex domain of $ℂ^{n}$ with smooth boundary. We consider the weighted mixed-norm spaces $A_{δ, k}^{p, q} (D)$ of holomorphic functions with norm $∥ f ∥_{p, q, δ, k} = (\sum_{| α | \leq k} ʃ_{0}^{r_{0}} (ʃ_{\partial D_{r}} | D^{α} {f |}^{p} d σ_{r} {)^{q / p} r^{δ q / p - 1} d r)}^{1 / q}$ . We prove that these spaces can be obtained by real interpolation between Bergman-Sobolev spaces $A_{δ, k}^{p} (D)$ and we give results about real and complex interpolation between them. We apply these results to prove that $A_{δ, k}^{p, q} (D)$ is the intersection of a Besov space $B_{s}^{p, q} (D)$ with the space of holomorphic functions on D. Further, we obtain several properties...

Calderón-Zygmund operators and unconditional bases of weighted Hardy spaces

J. García-Cuerva, K. Kazarian (1994)

Studia Mathematica

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We study sufficient conditions on the weight w, in terms of membership in the $A_{p}$ classes, for the spline wavelet systems to be unconditional bases of the weighted space $H^{p} (w)$ . The main tool to obtain these results is a very simple theory of regular Calderón-Zygmund operators.

On Topological Algebras

G. A. Stavrakas (1993)

Ευκλείδης Γ

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Molecular decompositions and embedding theorems for vector-valued Sobolev spaces with gradient norm

A. Pełczyński, M. Wojciechowski (1993)

Studia Mathematica

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Let E be a Banach space. Let $L ¹_{(1)} (ℝ^{d}, E)$ be the Sobolev space of E-valued functions on $ℝ^{d}$ with the norm $ʃ_{ℝ^{d}} ∥ f ∥_{E} d x + ʃ_{ℝ^{d}} ∥ \nabla f ∥_{E} d x = ∥ f ∥ ₁ + ∥ \nabla f ∥ ₁$ . It is proved that if $f \in L ¹_{(1)} (ℝ^{d}, E)$ then there exists a sequence $(g_{m}) \subset L_{(1)} ¹ (ℝ^{d}, E)$ such that $f = \sum_{m} g_{m}$ ; $\sum_{m} (∥ g_{m} ∥ ₁ + ∥ \nabla g_{m} ∥ ₁) < \infty$ ; and $∥ g_{m} ∥_{\infty}^{1 / d} ∥ g_{m} ∥ ₁^{(d - 1) / d} \leq b ∥ \nabla g_{m} ∥ ₁$ for m = 1, 2,..., where b is an absolute constant independent of f and E. The result is applied to prove various refinements of the Sobolev type embedding $L_{(1)} ¹ (ℝ^{d}, E) ↪ L ² (ℝ^{d}, E)$ . In particular, the embedding into Besov spaces $L ¹_{(1)} (ℝ^{d}, E) ↪ B_{p, 1}^{θ (p, d)} (ℝ^{d}, E)$ is proved, where $θ (p, d) = d (p^{- 1} + d^{- 1} - 1)$ for 1 < p ≤ d/(d-1), d=1,2,... The latter embedding in the scalar case is due to Bourgain...

Complemented ideals of group algebras

Andrew Kepert (1994)

Studia Mathematica

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The existence of a projection onto an ideal I of a commutative group algebra $L^{1} (G)$ depends on its hull Z(I) ⊆ Ĝ. Existing methods for constructing a projection onto I rely on a decomposition of Z(I) into simpler hulls, which are then reassembled one at a time, resulting in a chain of projections which can be composed to give a projection onto I. These methods are refined and examples are constructed to show that this approach does not work in general. Some answers are also given to previously...

Singularities of triples of vector fields on $R^{4}$ : the focusing stratum

Piotr Mormul (1988)

Studia Mathematica

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