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941.
942.
Gajath Gunatillake Mirjana Jovovic Wayne Smith 《Journal of Mathematical Analysis and Applications》2014
The operator that takes the function f to ψf°φ is a weighted composition operator. We study numerical ranges of some classes of weighted composition operators on H2, the Hardy–Hilbert space of the unit disc. We consider the case where φ is a rotation of the unit disc and identify a class of convexoid operators. In the case of isometric weighted composition operators we give a complete classification of their numerical ranges. We also consider the inclusion of zero in the interior of the numerical range. 相似文献
943.
944.
Let (X,T) be a topological dynamical system. A pair of points (x,y)∈X2 is called Banach proximal if for any ε>0, the set {n∈Z+:d(Tnx,Tny)<ε} has Banach density one. We study the structure of the Banach proximal relation. A useful tool is the notion of the support of a topological dynamical system. We show that a dynamical system is strongly proximal if and only if every pair in X2 is Banach proximal. A subset S of X is Banach scrambled if every two distinct points in S form a Banach proximal pair but not asymptotic. We construct a dynamical system with the whole space being a Banach scrambled set. Even though the Banach proximal relation of the full shift is of first category, it has a dense Mycielski invariant Banach scrambled set. We also show that for an interval map it is Li–Yorke chaotic if and only if it has a Cantor Banach scrambled set. 相似文献
945.
946.
Extending a classical linear result due to Hutton to a nonlinear setting, we prove that a continuous homogeneous polynomial between Banach spaces can be approximated by finite rank polynomials if and only if its adjoint can be approximated by finite rank linear operators. Among other consequences, we apply this result to generalize a classical result due to Aron and Schottenloher about the approximation property on spaces of polynomials and a recent result due to Çaliskan and Rueda about the quasi-approximation property on projective symmetric tensor products. 相似文献
947.
In this paper, we study positive Toeplitz operators on the Bergman space via their Berezin transforms. Surprisingly we show that the positivity of a Toeplitz operator on the Bergman space is not completely determined by the positivity of the Berezin transform of its symbol. In fact, we show that even if the minimal value of the Berezin transform of a quadratic polynomial of |z| on the unit disk is positive, the Toeplitz operator with the function as the symbol may not be positive. 相似文献
948.
949.
In this paper, we consider hypersurfaces in the unit lightlike sphere. The unit sphere can be canonically embedded in the lightcone and de Sitter space in Minkowski space. We investigate these hypersurfaces in the framework of the theory of Legendrian dualities between pseudo‐spheres in Minkowski space. 相似文献
950.
Christian Bargetz 《Mathematische Nachrichten》2014,287(1):10-22
In this article, we show that the Valdivia–Vogt structure table—containing the sequence space representations of the most used spaces of smooth functions appearing in the theory of distributions—can be interpreted as a commutative diagram, i.e., there is an isomorphism between the space of infinitely differentiable functions and the space , where s is the space of rapidly decreasing sequences, such that its restriction to the other function spaces in the structure table yields an isomorphism between these spaces of smooth functions and their sequence space representation. This result answers the corresponding question of Prof. Dietmar Vogt formulated on the conference “Functional Analysis: Applications to Complex Analysis and Partial Differential Equations” held in B?dlewo in May 2012. 相似文献