scholarly journals Fredholm theory of Toeplitz operators on doubling Fock Hilbert spaces

2020 ◽  
Vol 126 (3) ◽  
pp. 593-602
Author(s):  
Aamena Al-Qabani ◽  
Titus Hilberdink ◽  
Jani A. Virtanen
Keyword(s):  
Hilbert Spaces ◽  
Toeplitz Operators ◽  
Fredholm Theory ◽  
Fock Spaces ◽  
Essential Spectra ◽  
Weighted Fock Spaces ◽  
Special Case

We study the Fredholm properties of Toeplitz operators acting on doubling Fock Hilbert spaces, and describe their essential spectra for bounded symbols of vanishing oscillation. We also compute the index of these Toeplitz operators in the special case when $\varphi (z) = \lvert {z}\rvert^{\beta }$ with $\beta >0$. Our work extends the recent results on Toeplitz operators on the standard weighted Fock spaces to the setting of doubling Fock spaces.

scholarly journals Fredholm Toeplitz operators with VMO symbols and the duality of generalized Fock spaces with small exponents

2019 ◽  
Vol 150 (6) ◽  
pp. 3163-3186
Author(s):  
Zhangjian Hu ◽  
Jani A. Virtanen
Keyword(s):  
Toeplitz Operators ◽  
Complex Space ◽  
Function Spaces ◽  
Weight Functions ◽  
Fock Spaces ◽  
Mean Oscillation ◽  
Weighted Fock Spaces ◽  
First Time

AbstractWe characterize Fredholmness of Toeplitz operators acting on generalized Fock spaces of the n-dimensional complex space for symbols in the space of vanishing mean oscillation VMO. Our results extend the recent characterizations for Toeplitz operators on standard weighted Fock spaces to the setting of generalized weight functions and also allow for unbounded symbols in VMO for the first time. Another novelty is the treatment of small exponents 0 < p < 1, which to our knowledge has not been seen previously in the study of the Fredholm properties of Toeplitz operators on any function spaces. We accomplish this by describing the dual of the generalized Fock spaces with small exponents.

Unbounded Linear Operators

2018 ◽  
Author(s):  
D. E. Edmunds ◽  
W. D. Evans
Keyword(s):  
Hilbert Spaces ◽  
Linear Operators ◽  
Von Neumann ◽  
Limit Circle ◽  
Sectorial Operators ◽  
Closed Operators ◽  
The Stability ◽  
Symmetric Operators ◽  
Unbounded Linear Operators ◽  
Special Case

This chapter is concerned with closable and closed operators in Hilbert spaces, especially with the special classes of symmetric, J-symmetric, accretive and sectorial operators. The Stone–von Neumann theory of extensions of symmetric operators is treated as a special case of results for compatible adjoint pairs of closed operators. Also discussed in detail is the stability of closedness and self-adjointness under perturbations. The abstract results are applied to operators defined by second-order differential expressions, and Sims’ generalization of the Weyl limit-point, limit-circle characterization for symmetric expressions to J-symmetric expressions is proved.

scholarly journals Generalized n-circular projections on JB*-triples and Hilbert C0(Ω)-modules

2017 ◽  
Vol 4 (1) ◽  
pp. 109-120
Author(s):  
Dijana Ilišević ◽  
Chih-Neng Liu ◽  
Ngai-Ching Wong
Keyword(s):  
Banach Space ◽  
Hilbert Spaces ◽  
Orthogonal Projections ◽  
Geometric Properties ◽  
C Algebras ◽  
Structure Theorems ◽  
Special Case

Abstract Being expected as a Banach space substitute of the orthogonal projections on Hilbert spaces, generalized n-circular projections also extend the notion of generalized bicontractive projections on JB*-triples. In this paper, we study some geometric properties of JB*-triples related to them. In particular, we provide some structure theorems of generalized n-circular projections on an often mentioned special case of JB*-triples, i.e., Hilbert C*-modules over abelian C*-algebras C0(Ω).

Schatten-p class (0 < p ≤ ∞) Toeplitz operators on generalized Fock spaces

2015 ◽  
Vol 31 (4) ◽  
pp. 703-714 ◽  
Author(s):  
Lian Hua Xiao ◽  
Xiao Feng Wang ◽  
Jin Xia
Keyword(s):  
Toeplitz Operators ◽  
Fock Spaces
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