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On completely bounded bimodule maps over W*-algebras

Bojan Magajna (2003)

Studia Mathematica

It is proved that for a von Neumann algebra A ⊆ B(ℋ ) the subspace of normal maps is dense in the space of all completely bounded A-bimodule homomorphisms of B(ℋ ) in the point norm topology if and only if the same holds for the corresponding unit balls, which is the case if and only if A is atomic with no central summands of type I ∞ , ∞ . Then a duality result for normal operator modules is presented and applied to the following problem. Given an operator space X and a von Neumann algebra A, is the map...

On complex interpolation and spectral continuity

Karen Saxe (1998)

Studia Mathematica

Let [ X 0 , X 1 ] t , 0 ≤ t ≤ 1, be Banach spaces obtained via complex interpolation. With suitable hypotheses, linear operators T that act boundedly on both X 0 and X 1 will act boundedly on each [ X 0 , X 1 ] t . Let T t denote such an operator when considered on [ X 0 , X 1 ] t , and σ ( T t ) denote its spectrum. We are motivated by the question of whether or not the map t → σ ( T t ) is continuous on (0,1); this question remains open. In this paper, we study continuity of two related maps: t → ( σ ( T t ) ) ∧ (polynomially convex hull) and t → ∂ e ( σ ( T t ) ) (boundary of the polynomially convex...

On conditions for the boundedness of the Weyl fractional integral on weighted L p spaces

Liliana De Rosa, Alberto de la Torre (2004)

Commentationes Mathematicae Universitatis Carolinae

In this paper we give a sufficient condition on the pair of weights ( w , v ) for the boundedness of the Weyl fractional integral I α + from L p ( v ) into L p ( w ) . Under some restrictions on w and v , this condition is also necessary. Besides, it allows us to show that for any p : 1 ≤ p < ∞ there exist non-trivial weights w such that I α + is bounded from L p ( w ) into itself, even in the case α > 1 .

On contractive projections in Hardy spaces

Florence Lancien, Beata Randrianantoanina, Eric Ricard (2005)

Studia Mathematica

We prove a conjecture of Wojtaszczyk that for 1 ≤ p < ∞, p ≠ 2, H p ( ) does not admit any norm one projections with dimension of the range finite and greater than 1. This implies in particular that for 1 ≤ p < ∞, p ≠ 2, H p does not admit a Schauder basis with constant one.

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