In this work, we prove existence and uniqueness fixed point theorems under Banach and Kannan type contractions on $ \mathcal{C}^{\star} $-algebra-valued bipolar metric spaces. To strengthen our main ...results, an appropriate example and an effective application are presented.
In this article, we study the non-Newtonian version of
algebras. Further, we generalize some results which hold for the classical
algebras. We also discuss some illustrative examples to show accuracy ...and effectiveness of the new findings. If we take the identity function I instead of the generators α and β in the construction of the set
then non-Newtonian
algebras turn into the classical
algebras, so our results are stronger than some knowledge and facts in the most existing literature.
We study residually finite-dimensional (or RFD) operator algebras which may not be self-adjoint. An operator algebra may be RFD while simultaneously possessing completely isometric representations ...whose generating C⁎-algebra is not RFD. This has provided many hurdles in characterizing residual finite-dimensionality for operator algebras. To better understand the elusive behavior, we explore the C⁎-covers of an operator algebra. First, we equate the collection of C⁎-covers with a complete lattice arising from the spectrum of the maximal C⁎-cover. This allows us to identify a largest RFD C⁎-cover whenever the underlying operator algebra is RFD. The largest RFD C⁎-cover is shown to be similar to the maximal C⁎-cover in several different facets and this provides supporting evidence to a previous query of whether an RFD operator algebra always possesses an RFD maximal C⁎-cover. In closing, we present a non self-adjoint version of Hadwin's characterization of separable RFD C⁎-algebras.
It is a fact that $ C^* $-algebra-valued metric space is more general and hence the results in this space are proper improvements of their corresponding ideas in standard metric spaces. With this ...motivation, this paper focuses on introducing the concepts of $ C^* $-algebra-valued $ F $-contractions and $ C^* $-algebra-valued $ F $-Suzuki contractions and then investigates novel criteria for the existence of fixed points for such mappings. It is observed that the notions examined herein harmonize and refine a number of existing fixed point results in the related literature. A few of these special cases are highlighted and analyzed as some consequences of our main ideas. Nontrivial comparative illustrations are constructed to support the hypotheses and indicate the preeminence of the obtained key concepts. From application viewpoints, one of our results is applied to discuss new conditions for solving a Volterra-type integral equation.
We construct the reduced and essential C*-algebra of a Fell bundle over an étale groupoid (in full generality, without any second countability, local compactness or Hausdorff assumptions, even on the ...unit space) directly from sections under convolution. This eliminates the j-map commonly seen in the groupoid and Fell bundle C*-algebra literature. We further show how multiplier algebras and other Banach *-bimodules can again be constructed directly from sections. Finally, we extend Varela's morphisms from C*-bundles to Fell bundles, thus making the reduced C*-algebra construction functorial.
In this manuscript, we prove some fixed point theorems on C -algebra-valued partial b-metric spaces by using generalized contraction. We give support and suitable examples of our main results. ...Moreover, we present a generative application of the main results.
We study the natural representation of the topological full group of an ample Hausdorff groupoid in the groupoid's complex Steinberg algebra and in its full and reduced C*-algebras. We characterise ...precisely when this representation is injective and show that it is rarely surjective. We then restrict our attention to discrete groupoids, which provide unexpected insight into the behaviour of the representation of the topological full group in the full and reduced groupoid C*-algebras. We show that the image of the representation is not dense in the full groupoid C*-algebra unless the groupoid is a group, and we provide an example showing that the image of the representation may still be dense in the reduced groupoid C*-algebra even when the groupoid is not a group.
In the present manuscript, notions of $ C^* $-algebra valued $ \mathcal{R} $-metric space and $ C^* $-algebra valued $ \mathcal{R} $-contractive map are introduced along with some fixed point results ...which in turn generalizes and unifies certain well known results in the existing literature. Further, in support of the obtained results some illustrative examples have been provided.
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