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Bounded elements in certain topological partial *-algebras

Jean-Pierre Antoine, Camillo Trapani, Francesco Tschinke (2011)

Studia Mathematica

We continue our study of topological partial *-algebras, focusing on the interplay between various partial multiplications. The special case of partial *-algebras of operators is examined first, in particular the link between strong and weak multiplications, on one hand, and invariant positive sesquilinear (ips) forms, on the other. Then the analysis is extended to abstract topological partial *-algebras, emphasizing the crucial role played by appropriate bounded elements, called ℳ-bounded. Finally,...

Bounded evaluation operators from H p into ℓ q

Martin Smith (2007)

Studia Mathematica

Given 0 < p,q < ∞ and any sequence z = zₙ in the unit disc , we define an operator from functions on to sequences by T z , p ( f ) = ( 1 - | z ₙ | ² ) 1 / p f ( z ₙ ) . Necessary and sufficient conditions on zₙ are given such that T z , p maps the Hardy space H p boundedly into the sequence space ℓ q . A corresponding result for Bergman spaces is also stated.

Bounded linear functionals on the space of Henstock-Kurzweil integrable functions

Tuo-Yeong Lee (2009)

Czechoslovak Mathematical Journal

Applying a simple integration by parts formula for the Henstock-Kurzweil integral, we obtain a simple proof of the Riesz representation theorem for the space of Henstock-Kurzweil integrable functions. Consequently, we give sufficient conditions for the existence and equality of two iterated Henstock-Kurzweil integrals.

Bounded linear maps between (LF)-spaces.

Angela A. Albanese (2003)

RACSAM

Characterizations of pairs (E,F) of complete (LF)?spaces such that every continuous linear map from E to F maps a 0?neighbourhood of E into a bounded subset of F are given. The case of sequence (LF)?spaces is also considered. These results are similar to the ones due to D. Vogt in the case E and F are Fréchet spaces. The research continues work of J. Bonet, A. Galbis, S. Önal, T. Terzioglu and D. Vogt.

Bounded operators on weighted spaces of holomorphic functions on the upper half-plane

Mohammad Ali Ardalani, Wolfgang Lusky (2012)

Studia Mathematica

Let v be a standard weight on the upper half-plane , i.e. v: → ]0,∞[ is continuous and satisfies v(w) = v(i Im w), w ∈ , v(it) ≥ v(is) if t ≥ s > 0 and l i m t → 0 v ( i t ) = 0 . Put v₁(w) = Im wv(w), w ∈ . We characterize boundedness and surjectivity of the differentiation operator D: Hv() → Hv₁(). For example we show that D is bounded if and only if v is at most of moderate growth. We also study composition operators on Hv().

Currently displaying 281 – 300 of 352