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Linear operators on non-locally convex Orlicz spaces

Marian Nowak, Agnieszka Oelke (2008)

Banach Center Publications

We study linear operators from a non-locally convex Orlicz space L Φ to a Banach space ( X , | | · | | X ) . Recall that a linear operator T : L Φ X is said to be σ-smooth whenever u ( o ) 0 in L Φ implies | | T ( u ) | | X 0 . It is shown that every σ-smooth operator T : L Φ X factors through the inclusion map j : L Φ L Φ ̅ , where Φ̅ denotes the convex minorant of Φ. We obtain the Bochner integral representation of σ-smooth operators T : L Φ X . This extends some earlier results of J. J. Uhl concerning the Bochner integral representation of linear operators defined on a locally convex...

Linear topological invariants of spaces of holomorphic functions in infinite dimension.

Nguyen Minh Ha, Le Mau Hai (1995)

Publicacions Matemàtiques

It is shown that if E is a Frechet space with the strong dual E* then Hb(E*), the space of holomorphic functions on E* which are bounded on every bounded set in E*, has the property (DN) when E ∈ (DN) and that Hb(E*) ∈ (Ω) when E ∈ (Ω) and either E* has an absolute basis or E is a Hilbert-Frechet-Montel space. Moreover the complementness of ideals J(V) consisting of holomorphic functions on E* which are equal to 0 on V in H(E*) for every nuclear Frechet space E with E ∈ (DN) ∩ (Ω) is stablished...

Linear topological properties of the Lumer-Smirnov class of the polydisc

Marek Nawrocki (1992)

Studia Mathematica

Linear topological properties of the Lumer-Smirnov class L N ( n ) of the unit polydisc n are studied. The topological dual and the Fréchet envelope are described. It is proved that L N ( n ) has a weak basis but it is nonseparable in its original topology. Moreover, it is shown that the Orlicz-Pettis theorem fails for L N ( n ) .

Linearity in non-linear problems.

Richard Aron, Domingo García, Manuel Maestre (2001)

RACSAM

Estudiamos algunas situaciones donde encontramos un problema que, a primera vista, parece no tener solución. Pero, de hecho, existe un subespacio vectorial grande de soluciones del mismo.

Currently displaying 221 – 240 of 366