Characterization of convolution operators on spaces ofC ?-functions admitting a continuous linear right inverse

1987 ◽  
Vol 279 (1) ◽  
pp. 141-155 ◽  
Author(s):  
Reinhold Meise ◽  
Dietmar Vogt
Keyword(s):  
Continuous Linear ◽  
Convolution Operators

scholarly journals Convolution operators on weighted spaces of continuous functions and supremal convolution

2019 ◽  
Vol 199 (4) ◽  
pp. 1547-1569
Author(s):  
T. Kleiner ◽  
R. Hilfer
Keyword(s):  
Continuous Functions ◽  
Weighted Spaces ◽  
Constructive Method ◽  
Convolution Operators ◽  
Linear Combinations ◽  
The Third ◽  
Bounded Set ◽  
Spaces Of Continuous Functions ◽  
Bounded Sets

AbstractThe convolution of two weighted balls of measures is proved to be contained in a third weighted ball if and only if the supremal convolution of the corresponding two weights is less than or equal to the third weight. Here supremal convolution is introduced as a type of convolution in which integration is replaced with supremum formation. Invoking duality the equivalence implies a characterization of equicontinuity of weight-bounded sets of convolution operators having weighted spaces of continuous functions as domain and range. The overall result is a constructive method to define weighted spaces on which a given set of convolution operators acts as an equicontinuous family of endomorphisms. The result is applied to linear combinations of fractional Weyl integrals and derivatives with orders and coefficients from a given bounded set.

Paleokarst reservoirs: Efficient and flexible characterization using point-spread function-based convolution modeling

2021 ◽  
pp. 1-65
Author(s):  
Kristian Jensen ◽  
Martin Kyrkjebø Johansen ◽  
Isabelle Lecomte ◽  
Xavier Janson ◽  
Jan Tveranger ◽  
...  
Keyword(s):  
Seismic Data ◽  
Convolution Operators ◽  
Point Spread Functions ◽  
Point Spread ◽  
Spread Function ◽  
Open Cavities ◽  
Modeling Experiment ◽  
Seismic Characterization ◽  
Seismic Images

Paleokarst originate from collapse, degradation and infill of karstified rock, and typically feature spatially heterogeneous elements such as breakdown products, sediment infills and preserved open cavities on all scales. Paleokarst may further contain aquifer or hydrocarbon reservoirs as well as pose a drilling hazard during exploration. Seismic characterization of paleokarst reservoirs therefore remains both a challenging and important task. We illustrate how the application of 2(3)D spatial convolution operators, referred to as point-spread functions (PSFs), allows for seismic modeling of complex and heterogeneous paleokarst geology at a cost equivalent to conventional repeated 1D convolution. Unlike the latter, which only considers vertical resolution effects, PSF-based convolution modeling yields simulated prestack depth migrated images accounting for 3D resolution effects both vertically and laterally caused by acquisition geometries, frequency-band limitations, and propagation effects in the overburden. We confirm the validity of the approach by a comparison of modeled results to results obtained from a published physical modeling experiment. Finally, we present four additional separate case studies to highlight the usability and flexibility of the approach by assessing different issues and challenges pertaining to characterizing and interpreting seismic features of paleokarst. Through PSF-based convolution modeling, geoscientists working with paleokarst seismic data may be better able to understand how various acquisition and modeling parameters affect seismic images of paleokarst geology.

scholarly journals On a characterization of compactness and the Abel-Poisson summability of fourier coefficients in Banach spaces

Filomat ◽  
2016 ◽  
Vol 30 (4) ◽  
pp. 1061-1068
Author(s):  
Seda Öztürk
Keyword(s):  
Banach Space ◽  
Topological Group ◽  
Integral Representation ◽  
Unit Circle ◽  
Banach Spaces ◽  
Fourier Coefficients ◽  
Linear Representation ◽  
Complex Banach Space ◽  
Continuous Linear

In this paper, for an isometric strongly continuous linear representation denoted by ? of the topological group of the unit circle in complex Banach space, we study an integral representation for Abel-Poisson mean A?r (x) of the Fourier coefficients family of an element x, and it is proved that this family is Abel-Poisson summable to x. Finally, we give some tests which are related to characterizations of relatively compactness of a subset by means of Abel-Poisson operator A?r and ?.

scholarly journals Maximal ideals in some F-algebras of holomorphic functions

Filomat ◽  
2015 ◽  
Vol 29 (1) ◽  
pp. 1-5 ◽  
Author(s):  
Romeo Mestrovic
Keyword(s):  
Linear Functional ◽  
Holomorphic Functions ◽  
Complete Characterization ◽  
Open Unit ◽  
Continuous Linear ◽  
Linear Functionals ◽  
Continuous Linear Functional ◽  
Maximal Ideals ◽  
Algebras Of Holomorphic Functions

For 1 < p < ?, the Privalov class Np consists of all holomorphic functions f on the open unit disk D of the complex plane C such that sup 0?r<1?2?0 (log+ |f(rei?)j|p d?/2? < + ? M. Stoll [16] showed that the space Np with the topology given by the metric dp defined as dp(f,g) = (?2?0 (log(1 + |f*(ei?) - g*(ei?)|))p d?/2?)1/p, f,g ? Np; becomes an F-algebra. Since the map f ? dp(f,0) (f ? Np) is not a norm, Np is not a Banach algebra. Here we investigate the structure of maximal ideals of the algebras Np (1 < p < ?). We also give a complete characterization of multiplicative linear functionals on the spaces Np. As an application, we show that there exists a maximal ideal of Np which is not the kernel of a multiplicative continuous linear functional on Np.

Characterization of linear mappings on (Banach) ⋆-algebras by similar properties to derivations

2020 ◽  
Vol 70 (4) ◽  
pp. 1003-1011
Author(s):  
Behrooz Fadaee ◽  
Kamal Fallahi ◽  
Hoger Ghahramani
Keyword(s):  
Banach Algebra ◽  
Complex Variable ◽  
Operator Algebras ◽  
Banach Algebras ◽  
Jordan Derivation ◽  
Continuous Linear ◽  
Linear Map ◽  
Standard Operator ◽  
Standard Operator Algebras

AbstractLet 𝓐 be a ⋆-algebra, δ : 𝓐 → 𝓐 be a linear map, and z ∈ 𝓐 be fixed. We consider the condition that δ satisfies xδ(y)⋆ + δ(x)y⋆ = δ(z) (x⋆δ(y) + δ(x)⋆y = δ(z)) whenever xy⋆ = z (x⋆y = z), and under several conditions on 𝓐, δ and z we characterize the structure of δ. In particular, we prove that if 𝓐 is a Banach ⋆-algebra, δ is a continuous linear map, and z is a left (right) separating point of 𝓐, then δ is a Jordan derivation. Our proof is based on complex variable techniques. Also, we describe a linear map δ satisfying the above conditions with z = 0 on two classes of ⋆-algebras: zero product determined algebras and standard operator algebras.

scholarly journals Linear Maps Which are Anti-derivable at Zero

2020 ◽  
Vol 43 (6) ◽  
pp. 4315-4334
Author(s):  
Doha Adel Abulhamil ◽  
Fatmah B. Jamjoom ◽  
Antonio M. Peralta
Keyword(s):  
Linear Operator ◽  
Bounded Linear Operator ◽  
Complete Characterization ◽  
Linear Operators ◽  
Continuous Linear ◽  
Bounded Linear ◽  
Linear Maps ◽  
Continuous Linear Operators

Abstract Let $$T:A\rightarrow X$$ T : A → X be a bounded linear operator, where A is a $$\hbox {C}^*$$ C ∗ -algebra, and X denotes an essential Banach A-bimodule. We prove that the following statements are equivalent: (a) T is anti-derivable at zero (i.e., $$ab =0$$ a b = 0 in A implies $$T(b) a + b T(a)=0$$ T ( b ) a + b T ( a ) = 0 ); (b) There exist an anti-derivation $$d:A\rightarrow X^{**}$$ d : A → X ∗ ∗ and an element $$\xi \in X^{**}$$ ξ ∈ X ∗ ∗ satisfying $$\xi a = a \xi ,$$ ξ a = a ξ , $$\xi [a,b]=0,$$ ξ [ a , b ] = 0 , $$T(a b) = b T(a) + T(b) a - b \xi a,$$ T ( a b ) = b T ( a ) + T ( b ) a - b ξ a , and $$T(a) = d(a) + \xi a,$$ T ( a ) = d ( a ) + ξ a , for all $$a,b\in A$$ a , b ∈ A . We also prove a similar equivalence when X is replaced with $$A^{**}$$ A ∗ ∗ . This provides a complete characterization of those bounded linear maps from A into X or into $$A^{**}$$ A ∗ ∗ which are anti-derivable at zero. We also present a complete characterization of those continuous linear operators which are $$^*$$ ∗ -anti-derivable at zero.

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