On Beurling-type theorems in weighted and Bergman spaces

We prove that analytic operators satisfying certain series of operator inequalities possess the wandering subspace property. As a corollary, we obtain Beurling-type theorems for invariant subspaces in certain weighted and Bergman spaces.

     

A note on Besov-Morrey spaces and Triebel-Lizorkin-Morrey spaces

In the present paper, we obtain three independent results on the Besov-Morrey spaces and the Triebel-Lizorkin-Morrey spaces. That is, we are going to obtain the characterization of local means, the boundedness of pseudo-differential operators and the characterization of the Hardy-Morrey spaces. By using the maximal estimate and the molecular decomposition, we shall integrate and extend the known results on these spaces.     

A counterexample for boundedness of pseudo-differential operators on modulation spaces

We prove that pseudo-differential operators with symbols in the class ( ) are not always bounded on the modulation space ().

     

On the Ornstein-Uhlenbeck operator in spaces with respect to invariant measures

We consider a class of elliptic and parabolic differential operators with unbounded coefficients in , and we study the properties of the realization of such operators in suitable weighted spaces.

     

On the comparison of the spaces

The notion of -variation and the space arise in the study of regularity properties of solutions to perturbed conservation laws. In this article we show that this notion is equivalent to variation in the regular sense, and therefore the space is the same as the space in the sense of Cesari-Tonelli. We also point out some connection between the space and the Favard classes for translation semigroups.

     

Renorming of spaces

If is a scattered Eberlein compact space, then admits an equivalent dual norm that is uniformly rotund in every direction. The same is shown for the dual to the Johnson-Lindenstrauss space .

     

The relationship between fragmentable spaces and class spaces

In this note, we show that each fragmentable space introduced by Jayne and Rogers in 1985 is of class which was introduced by Kenderov in 1984. Our example shows that a space which is of class may not be a fragmentable space.

     

Rademacher bounded families of operators on

We give a characterization of R-bounded families of operators on We then use this result to study sectorial operators on . We show that if is an R-sectorial operator on , then, for any there is an invertible operator with such that for some strictly positive Borel function , contains the weighted -space

     

Bilinear pseudodifferential operators with forbidden symbols on Lipschitz and Besov spaces

We show that bilinear pseudodifferential operators with symbols in the forbidden class are bounded on products of Lipschitz and Besov spaces.     

Bilinear pseudo-differential operators on local hardy spaces

In this paper, the authors consider a class of bilinear pseudo-differential operators with symbols of order 0 and type (1, 0) in the sense of Ho¨rmander and use the atomic decompositions of local Hardy spaces to establish the boundedness of the bilinear pseudo-differential operators and the bilinear singular integral operators on the product of local Hardy spaces.     

Essential numerical range of elementary operators

Let and denote two -tuples of operators with and Let denote the elementary operators defined on the Hilbert-Schmidt class by We show that

Here is the essential numerical range, is the joint numerical range and is the joint essential numerical range.

     

On the classes of spaces

The two better-known ways of understanding the notion of local unconditional structure allow us to define successive extensions of the well-known class of the spaces of Lindenstrauss and Pelczynski. This paper also studies stability properties of these classes under ultrapowers, biduals and complemented subspaces.

     

Locally finite dimensional shift-invariant spaces in

We prove that a locally finite dimensional shift-invariant linear space of distributions must be a linear subspace of some shift-invariant space generated by finitely many compactly supported distributions. If the locally finite dimensional shift-invariant space is a subspace of the Hölder continuous space or the fractional Sobolev space , then the superspace can be chosen to be or , respectively.

     

Noncommutative spaces

Let be a von Neumann algebra with a faithful, finite, normal tracial state , and let be a finite, maximal subdiagonal algebra of . Let be the closure of in the noncommutative Lebesgue space . Then possesses several of the properties of the classical Hardy space on the circle, including a commutant lifting theorem, some results on Toeplitz operators, an factorization theorem, Nehari's Theorem, and harmonic conjugates which are bounded.

     

-theory of -pseudo-differential algebras

We are concerned with the so-called -pseudo-differential calculus. We describe the spectrum of the unital and commutative -algebra given by the norm closure of the space of -order pseudo-differential operators modulo compact operators; other related algebras are also considered. Finally, their -theory is computed.

     

Generalized Anti-Wick Operators with Symbols in Distributional Sobolev spaces

Generalized Anti-Wick operators are introduced as a class of pseudodifferential operators which depend on a symbol and two different window functions. Using symbols in Sobolev spaces with negative smoothness and windows in so-called modulation spaces, we derive new conditions for the boundedness on L² of such operators and for their membership in the Schatten classes. These results extend and refine results contained in [20], [10], [5], [4], and [14].     

Compact sets of compact operators in absence of

We characterize the compactness of a subset of compact operators between Banach spaces when the domain space does not have a copy of

     

Nonnormal spaces with countable extent

Examples of spaces are constructed for which is not normal but all closed discrete subsets are countable. A monolithic example is constructed in ZFC and a separable first countable example is constructed using .

     

The largest linear space of operators satisfying the Daugavet equation in

We find the largest linear space of bounded linear operators on that, being restricted to any , , satisfy the Daugavet equation.