Institute of Mathematics AS CR, v. v. i.
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The Banach algebra and tame functionals
No full textsummary:We give an affirmative answer to a question due to M. Megrelishvili, and show that for every locally compact group we have Tame Tame, which means that a functional is tame over if and only if it is tame as a function over . In fact, it is proven that for every norm-saturated, convex vector bornology on RUC, being small as a function and as a functional is the same. This proves that Asp Asp and reaffirms a well-known, similar result which states that WAP WAP
Recurrence and mixing recurrence of multiplication operators
Get PDFsummary:Let be a Banach space, the algebra of bounded linear operators on and an admissible Banach ideal of . For , let and denote the left and right multiplication defined by and , respectively. In this paper, we study the transmission of some concepts related to recurrent operators between , and their elementary operators and . In particular, we give necessary and sufficient conditions for and to be sequentially recurrent. Furthermore, we prove that is recurrent if and only if is recurrent on . Moreover, we introduce the notion of a mixing recurrent operator and we show that is mixing recurrent if and only if is mixing recurrent
Convex -fuzzy remote neighborhood operators
Get PDFsummary:In this paper, two kinds of remote neighborhood operators in -fuzzy convex spaces are proposed, which are called convex -fuzzy remote neighborhood operators. It is proved that these two kinds of convex -fuzzy remote neighborhood operators can be used to characterize -fuzzy convex structures. In addition, the lattice structures of two kinds of convex -fuzzy remote neighborhood operators are also given
Quantized cooperative output regulation of continuous-time multi-agent systems over switching graph
Get PDFsummary:This paper investigates the problem of quantized cooperative output regulation of linear multi-agent systems with switching graphs. A novel dynamic encoding-decoding scheme with a finite communication bandwidth is designed. Leveraging this scheme, a distributed protocol is proposed, ensuring asymptotic convergence of the tracking error under both bounded and unbounded link failure durations. Compared with the existing quantized control work of MASs, the semi-global assumption of initial conditions is not required, and the communication graph is only required to be jointly connected. Finally, two simulation examples demonstrate the effectiveness of the proposed distributed protocol for bounded and unbounded link failure durations
Maximal non-pseudovaluation subrings of an integral domain
No full textsummary:The notion of maximal non-pseudovaluation subring of an integral domain is introduced and studied. Let be an extension of domains. Then is called a maximal non-pseudovaluation subring of if is not a pseudovaluation subring of , and for any ring such that , is a pseudovaluation subring of . We show that if is not local, then there no such exists between and . We also characterize maximal non-pseudovaluation subrings of a local integral domain
Bilinear fractional Hardy-type operators with rough kernels on central Morrey spaces with variable exponents
No full textsummary:We introduce a type of -dimensional bilinear fractional Hardy-type operators with rough kernels and prove the boundedness of these operators and their commutators on central Morrey spaces with variable exponents. Furthermore, the similar definitions and results of multilinear fractional Hardy-type operators with rough kernels are obtained
-basic construction between non-balanced quantum doubles
No full textsummary:For finite groups , and the right -action on by group automorphisms, the non-balanced quantum double is defined as the crossed product . We firstly prove that is a finite-dimensional Hopf -algebra. For any subgroup of , can be defined as a Hopf -subalgebra of in the natural way. Then there is a conditonal expectation from onto and the index is . Moreover, we prove that an associated natural inclusion of non-balanced quantum doubles is the crossed product by the group algebra
Permutations With Prescribed Cycle Lengths
No full textsummary:Článek se zabývá zkoumáním a počítáním permutací, jejichž cykly mají předepsané délky. V první části představíme třídu permutací složených pouze z jednocyklů a dvojcyklů a ukážeme některé související úlohy. Druhá část je věnována dalším třídám permutací a postupům, jak zjistit jejich počty. Vedle kombinatorického přístupu využíváme též analytický přístup pracující s exponenciálními generujícími funkcemi