We define positive Toeplitz operators between harmonic Bergman–Besov spaces $$b^p_\alpha $$ on the unit ball of $${\mathbb {R}}^n$$ for full ranges parameters $$0<p<\infty , $$\alpha \in {\mathbb {R}}$$ . give characterizations bounded and compact taking one space into another in terms Carleson vanishing measures. also a operator $$b^{2}_{\alpha }$$ to be Schatten class $$S_{p}$$ averaging func...

in this paper, we considered composition operators on weighted hilbert spaces of analytic functions and  observed that a formula for the  essential norm, gives a hilbert-schmidt characterization and characterizes the membership in schatten-class for these operators. also, closed range composition operators  are investigated.

Dedicated to my " father " Leonard Gross, and to the memory of my " grandfather " Irving Segal. Contents 1. Introduction 1 2. Basics of holomorphic function spaces 2 3. Examples of holomorphic function spaces 7 4. A special property of the Segal-Bargmann and weighted Bergman spaces 12 5. Canonical commutation relations 16 6. The Segal-Bargmann transform 21 7. Quantum mechanics and quantization ...

Multiple cues are typically available for perceiving the 3D slant of surfaces, and slant perception has been used as a test case for investigating cue integration. Previous evidence suggests that texture and stereo slant cues contribute in an optimal Bayesian manner. We tested whether a Bayesian model could also account for perceptual underestimation of slant from texture. One explanation propo...

We study connections between operator theoretic properties of Toeplitz operators acting on suitable Besikovitch spaces and factorizations of their symbols which are matrix valued almost periodic functions of several real variables. Among other things, we establish the existence of a twisted canonical factorization for locally sectorial symbols, and characterize one-sided invertibility of Toepli...

Let Tf denote the Toeplitz operator with symbol function f on the Bergman space La(B, dv) of the unit ball in C . It is a natural problem in the theory of Toeplitz operators to determine the norm closure of the set {Tf : f ∈ L∞(B, dv)} in B(La(B, dv)). We show that the norm closure of {Tf : f ∈ L∞(B, dv)} actually coincides with the Toeplitz algebra T , i.e., the C∗-algebra generated by {Tf : f...

Certainly the best understood commutative Banach algebras are those that consist of all the continuous complex-valued functions on a compact Hausdorff space. Indeed, most self-adjoint phenomena involving them have been thoroughly investigated. In particular, the study of their representation theory as operators on a Hilbert space, which is essentially the spectral theory for normal operators, s...

For f in L∞, the space of essentially bounded Lebesgue measurable functions on the unit circle, ∂D, the Toeplitz operator with symbol f is the operator Tf on the Hardy space H2 of the unit circle defined by Tfh = P (fh). Here P denotes the orthogonal projection in L2 with range H2. There are many fascinating problems about Toeplitz operators ([3], [6], [7] and [20]). In this paper we shall conc...

In this paper we establish a tractable and explicit criterion for the hyponormality of arbitrary trigonometric Toeplitz operators, i.e., Toeplitz operators Tφ with trigonometric polynomial symbols φ. Our criterion involves the zeros of an analytic polynomial f induced by the Fourier coefficients of φ. Moreover the rank of the selfcommutator of Tφ is computed from the number of zeros of f in the...

there are many different ways to subdivide the spectrum of a bounded linear operator; some of them aremotivated by applications to physics (in particular, quantum mechanics). in this study, the relationship betweenthe subdivisions of spectrum which are not required to be disjoint and goldberg's classification are given.moreover, these subdivisions for some summability methods are studied.