Certain Banach-Space Operators Acting on Free Poisson Elements Induced by Orthogonal Projections

2020 ◽  
pp. 1-48
Author(s):  
Ilwoo Cho
Keyword(s):  
Banach Space ◽  
Orthogonal Projections ◽  
Banach Space Operators

scholarly journals On the essential spectrum of Banach-space operators

2000 ◽  
Vol 43 (3) ◽  
pp. 511-528 ◽  
Author(s):  
Jörg Eschmeier
Keyword(s):  
Banach Space ◽  
Essential Spectrum ◽  
Negative Index ◽  
Resolvent Set ◽  
Image Position ◽  
Nuclear Spaces ◽  
Simply Connected ◽  
Banach Space Operators

AbstractLet T and S be quasisimilar operators on a Banach space X. A well-known result of Herrero shows that each component of the essential spectrum of T meets the essential spectrum of S. Herrero used that, for an n-multicyclic operator, the components of the essential resolvent set with maximal negative index are simply connected. We give new and conceptually simpler proofs for both of Herrero's results based on the observation that on the essential resolvent set of T the section spaces of the sheavesare complete nuclear spaces that are topologically dual to each other. Other concrete applications of this result are given.

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).

scholarly journals Modified cauchy kernels and functional calculus for operators on Banach space

1997 ◽  
Vol 63 (1) ◽  
pp. 91-99 ◽  
Author(s):  
Edwin Franks
Keyword(s):  
Banach Space ◽  
Functional Calculus ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Cauchy Kernel ◽  
Necessary And Sufficient ◽  
Banach Space Operators

AbstractIn Banach space operators with a bounded H∞ functional calculus, Cowling et al. provide some necessary and sufficient conditions for a type-ω operator to have a bounded H∞ functional calculus. We provide an alternate development of some of their ideas using a modified Cauchy kernel which is L1 with respect to the measure ]dz]/]z]. The method is direct and has the advantage that no transforms of the functions are necessary.

scholarly journals A Unifying Approach to Weyl Type Theorems for Banach Space Operators

2013 ◽  
Vol 77 (3) ◽  
pp. 371-384 ◽  
Author(s):  
Pietro Aiena ◽  
Jesús R. Guillén ◽  
Pedro Peña
Keyword(s):  
Banach Space ◽  
Weyl Type Theorems ◽  
Banach Space Operators

scholarly journals THE CLOSED RANGE PROPERTY FOR BANACH SPACE OPERATORS

2008 ◽  
Vol 50 (1) ◽  
pp. 17-26 ◽  
Author(s):  
THOMAS L. MILLER ◽  
VLADIMIR MÜLLER
Keyword(s):  
Banach Space ◽  
Complex Plane ◽  
Open Subset ◽  
Weak Topology ◽  
Bounded Operator ◽  
Complex Banach Space ◽  
Fréchet Space ◽  
Closed Range ◽  
Open Set ◽  
Banach Space Operators

AbstractLetTbe a bounded operator on a complex Banach spaceX. LetVbe an open subset of the complex plane. We give a condition sufficient for the mappingf(z)↦ (T−z)f(z) to have closed range in the Fréchet spaceH(V,X) of analyticX-valued functions onV. Moreover, we show that there is a largest open setUfor which the mapf(z)↦ (T−z)f(z) has closed range inH(V,X) for allV⊆U. Finally, we establish analogous results in the setting of the weak–* topology onH(V, X*).

scholarly journals Property (Bb) and Tensor product

Filomat ◽  
2013 ◽  
Vol 27 (7) ◽  
pp. 1297-1303
Author(s):  
M.H.M. Rashid ◽  
T. Prasad
Keyword(s):  
Banach Space ◽  
Tensor Product ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Space Operator ◽  
Weyl Spectrum ◽  
Riesz Operators ◽  
Necessary And Sufficient ◽  
Banach Space Operators ◽  
Satisfy Property

In this paper, we find necessary and sufficient conditions for Banach Space operator to satisfy the property (Bb). Then we obtain, if Banach Space operators A ? B(X)and B ? B(Y) satisfy property (Bb) implies A x B satisfies property (Bb) if and only if the B-Weyl spectrum identity ?BW(A x B) = ?BW(A)?(B) U ?BW(B)?(A) holds. Perturbations by Riesz operators are considered.

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