Mathematics

In this paper, we present the complex interpolation of Besov and Triebel-Lizorkin spaces with generalized smoothness. In some particular cases these function spaces are just weighted Besov and Triebel-Lizorkin spaces. An application, we obtain the complex interpolation between the weighted Triebel-Lizorkin spaces F ˙ s 0 p 0 , q 0 ( ω 0 ) and F ˙ s 1 ∞, q 1 ( ω 1 ) with suitable assumptions on the parameters s 0 , s 1 , p 0 , q 0 and q 1 , and the pair of weights ( ω 0 , ω 1 ) .

We study the complex symmetric structure of weighted composition--differentiation operators of order n on the weighted Bergman spaces A 2 α with respect to some conjugations. Then we provide some examples of these operators.

In this paper we extensively investigate the class of conditionally positive definite operators, namely operators generating conditionally positive definite sequences. This class itself contains subnormal operators, 2 - and 3 -isometries and much more beyond them. Quite a large part of the paper is devoted to the study of conditionally positive definite sequences of exponential growth with emphasis put on finding criteria for their positive definiteness, where both notions are understood in the semigroup sense. As a consequence, we obtain semispectral and dilation type representations for conditionally positive definite operators. We also show that the class of conditionally positive definite operators is closed under the operation of taking powers. On the basis of Agler's hereditary functional calculus, we build an L ∞ (M) -functional calculus for operators of this class, where M is an associated semispectral measure. We provide a variety of applications of this calculus to inequalities involving polynomials and analytic functions. In addition, we derive new necessary and sufficient conditions for a conditionally positive definite operator to be a subnormal contraction (including a telescopic one).

We give a complete description of the structure of the connected components of the general linear group of a real hereditarily indecomposable Banach space, depending on the existence of complex structures on the space itself and on its hyperplanes. A side result is the fact that complex structures cannot exist simultaneously on such a space and on its hyperplanes.

Building on recent progress in constructing derivations on Fourier algebras, we provide the first examples of locally compact groups whose Fourier algebras support non-zero, alternating 2-cocycles; this is the first step in a larger project. Although such 2-cocycles can never be completely bounded, the operator space structure on the Fourier algebra plays a crucial role in our construction, as does the opposite operator space structure. Our construction has two main technical ingredients: we observe that certain estimates from [H. H. Lee, J. Ludwig, E. Samei, N. Spronk, Weak amenability of Fourier algebras and local synthesis of the anti-diagonal, Adv. Math., 292 (2016); arXiv 1502.05214] yield derivations that are "co-completely bounded" as maps from various Fourier algebras to their duals; and we establish a twisted inclusion result for certain operator space tensor products, which may be of independent interest.

In this paper, our aim is to introduce the concept of a frame in n-Hilbert space and describe some of their properties. We further discuss tight frame relative to n-Hilbert space. At the end, we study the relationship between frame and bounded linear operator in n-Hilbert space.

Frame Theory has a great revolution for recent years. This Theory has been extended from Hilbert spaces to Hilbert C ∗ -modules. The purpose of this paper is the introduction and the study of the new concept that of Continuous Controlled K-g-Frame for Hilbert C ∗ -Modules wich is a generalizations of discrete Controlled K-g-Frames in Hilbert C ∗ -Modules. Also we establish some results.

K -fusion frames are a generalization of fusion frames in frame theory. In this paper, we extend the concept of controlled fusion frames to controlled K -fusion frames, and we develop some results on the controlled K -fusion frames for Hilbert spaces, which generalized some well known of controlled fusion frames case. also we discuss some characterizations of controlled Bessel K -fusion sequences and of controlled Bessel K -fusion. Further, we analyse stability conditions of controlled K -fusion frames under perturbation.

In this paper we study the concept of controlled ∗ -operator frmae for En d ∗ A (H) . Also we discuss characterizations of controlled ∗ -operator frames and we give some properties

The notion of controlled frames for Hilbert spaces were introduced by Balazs, Antoine and Grybos to improve the numerical efficiency of iterative algorithms for inverting the frame operator. Controlled Frame Theory has a great revolution in recent years. This Theory have been extended from Hilbert spaces to Hilbert C ∗ -modules. In this paper we introduce and study the extension of this notion to integral frame for Hilbert C ∗ -module. Also we give some characterizations between integral frame in Hilbert C ∗ -module