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, 2021 In these notes, we introduce the reader to the categorical commutator theory (of subobjects), following the formal approach given by Mantovani and Metere in 2010.
A. Montoli +3 more
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Fractional operators and their commutators on generalized Orlicz spaces [PDF]
Opuscula Mathematica, 2022 In this paper we examine boundedness of fractional maximal operator. The main focus is on commutators and maximal commutators on generalized Orlicz spaces (also known as Musielak-Orlicz spaces) for fractional maximal functions and Riesz potentials.
Arttu Karppinen
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Associativity as commutativity [PDF]
Journal of Symbolic Logic, 2006 AbstractIt is shown that coherence conditions for monoidal categories concerning associativity are analogous to coherence conditions for symmetric strictly monoidal categories, where associativity arrows are identities. Mac Lane's pentagonal coherence condition for associativity is decomposed into conditions concerning commutativity, among which we ...
Došen, Kosta, Petrć, Zoran
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A Geometric Study of Commutator Subgroups [PDF]
, 2009 Let G be a group and G' its commutator subgroup. Commutator length (cl) and stable commutator length (scl) are naturally defined concepts for elements of G'. We study cl and scl for two classes of groups.
Zhuang, Dongping, Dongping Zhuang
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Writing commutators of commutators as products of cubes [PDF]
Communications in Algebra, 2021 It is known that commutators of commutators can be written as products of cubes, with the current upper bound on the number of cubes being 60. We discuss how proofs extracted via coset enumeration can be used to investigate this problem, and exhibit a rewriting using only 14 cubes.
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Operators with commutative commutants.
Michigan Mathematical Journal, 1988 Given operators M and N on a Hilbert space H, suppose that M (resp. N) is the direct sum of k (resp. n) copies of an operator A having a commutative commutant. Suppose further that m and k are countable cardinalities (or, any cardinalities if H is separable) and that N is a quasi-affine transform of M (i.e., \(NX=XM\) for some injective operator X with
Radjabalipour, M., Radjavi, H.
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Hypercyclicity Properties of Commutator Maps [PDF]
, 2017 We investigate the hypercyclic properties of commutator operators acting on separable Banach ideals of operators. As the main result we prove the commutator map induced by scalar multiples of the backward shift operator fails to be hypercyclic on the ...
Tylli, Hans-Olav +2 more
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A Characterization of Central BMO Space via the Commutator of Fractional Hardy Operator
Journal of Function Spaces, 2020 This paper is devoted in characterizing the central BMO ℝn space via the commutator of the fractional Hardy operator with rough kernel. Precisely, by a more explicit decomposition of the operator and the kernel function, we will show that if the symbol ...
Lei Zhang, Shaoguang Shi
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Some Notes on Relative Commutators
InPrime, 2020 Let G be a group and α ϵ Aut(G). An α-commutator of elements x, y ϵ G is defined as [x, y]α = x-1y-1xyα. In 2015, Barzegar et al. introduced an α-commutator of elements of G and defined a new generalization of nilpotent groups by using the definition of
Masoumeh Ganjali, Ahmad Erfanian
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SOLVABILITY OF FREE PRODUCTS, CAYLEY GRAPHS AND COMPLEXES [PDF]
Journal of Algebraic Systems, 2013 In this paper, we verify the solvability of free product of finite cyclic groups with topological methods. We use Cayley graphs and Everitt methods to construct suitable 2-complexes corresponding to the presentations of groups and their commutator ...
Hanieh Mirebrahimi, Fatemeh Ghanei
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