Compact Lambert type operators between two Lp spaces

Compact Composition Operators between Bloch Type Spaces in the Polydisk

and Applied Analysis 3 The following lemma is the crucial criterion for the compactness of Cφ, whose proof is an easy modification of the proof of Proposition 3.11 in 1 . Lemma 2.4. Assume that φ is a holomorphic self-map of D. Then Cφ : Bp → Bq is compact if and only if Cφ is bounded and for any bounded sequence {fm}m∈N in Bp which converges to zero uniformly on compact subsets of D, we have ∥...

Compact Composition Operators on Bloch Type Spaces

In this paper we characterize continuity and compactness of composition operators Cφ mapping the α-Bloch space into the μ-Bloch space, where μ is a weight defined on the unit disk D, in term of certain expression that involve the n-power of the symbol φ.

Compact Weighted Composition Operators and Multiplication Operators between Hardy Spaces

Spaces of Compact Operators

In this paper we study the structure of the Banach space K(E, F) of all compact linear operators between two Banach spaces E and F. We study three distinct problems: weak compactness in K(E, F), subspaces isomorphic to l~ and complementation of K(E, F) in L(E, F), the space of bounded linear operators. In § 2 we derive a simple characterization of the weakly compact subsets of K(E, F) using a c...

Norms of Positive Operators on LP-Spaces

Let 0 < T: LP(Y, v) -+ Lq(X, ) be a positive linear operator and let HITIP ,q denote its operator norm. In this paper a method is given to compute 1Tllp, q exactly or to bound 11Tllp q from above. As an application the exact norm 11VIlp,q of the Volterra operator Vf(x) = fo f(t)dt is computed.