Subnormality and cyclicity

Franciszek Hugon Szafraniec

Displaying similar documents to “Subnormality and cyclicity”

Note on cyclic decompositions of complete bipartite graphs into cubes

Dalibor Fronček (1999)

Discussiones Mathematicae Graph Theory

Similarity:

So far, the smallest complete bipartite graph which was known to have a cyclic decomposition into cubes $Q_{d}$ of a given dimension d was $K_{d 2^{d - 1}, d 2^{d - 2}}$ . We improve this result and show that also $K_{d 2^{d - 2}, d 2^{d - 2}}$ allows a cyclic decomposition into $Q_{d}$ . We also present a cyclic factorization of $K_{8, 8}$ into Q₄.

Kannan-type cyclic contraction results in $2$ -Menger space

Binayak S. Choudhury, Samir Kumar BHANDARI (2016)

Mathematica Bohemica

Similarity:

In this paper we establish Kannan-type cyclic contraction results in probabilistic 2-metric spaces. We use two different types of $t$ -norm in our theorems. In our first theorem we use a Hadzic-type $t$ -norm. We use the minimum $t$ -norm in our second theorem. We prove our second theorem by different arguments than the first theorem. A control function is used in our second theorem. These results generalize some existing results in probabilistic 2-metric spaces. Our results are illustrated with...

Circles passing through five or more integer points

Shaunna M. Plunkett-Levin (2013)

Acta Arithmetica

Similarity:

We find an improvement to Huxley and Konyagin’s current lower bound for the number of circles passing through five integer points. We conjecture that the improved lower bound is the asymptotic formula for the number of circles passing through five integer points. We generalise the result to circles passing through more than five integer points, giving the main theorem in terms of cyclic polygons with m integer point vertices. Theorem. Let m ≥ 4 be a fixed integer. Let $W_{m} (R)$ be the number...

Cyclic Type Fixed Point Results in 2-Menger Spaces

Binayak S. CHOUDHURY, Samir Kumar BHANDARI, Parbati SAHA (2015)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Similarity:

In this paper we introduce generalized cyclic contractions through $r$ number of subsets of a probabilistic 2-metric space and establish two fixed point results for such contractions. In our first theorem we use the Hadzic type $t$ -norm. In another theorem we use a control function with minimum $t$ -norm. Our results generalizes some existing fixed point theorem in 2-Menger spaces. The results are supported with some examples.

Bounded point evaluations for multicyclic operators

M. EL Guendafi, M. Mbekhta, E. H. Zerouali (2005)

Banach Center Publications

Similarity:

Let T be a multicyclic operator defined on some Banach space. Bounded point evaluations and analytic bounded point evaluations for T are defined to generalize the cyclic case. We extend some known results on cyclic operators to the more general setting of multicyclic operators on Banach spaces. In particular we show that if T satisfies Bishop’s property (β), then $ℬ_{a} = ℬ ∖ σ_{a p} (T)$ . We introduce the concept of analytic structures and we link it to different spectral quantities. We apply this concept...

The max norm in $R^{n}$ -isometries and measure

Regina Cohen, James W. Fickett (1982)

Colloquium Mathematicae

Similarity:

On the Rockafellar theorem for $Φ^{γ (\cdot, \cdot)}$ -monotone multifunctions

S. Rolewicz (2006)

Studia Mathematica

Similarity:

Let X be an arbitrary set, and γ: X × X → ℝ any function. Let Φ be a family of real-valued functions defined on X. Let $Γ : X \to 2^{Φ}$ be a cyclic $Φ^{γ (\cdot, \cdot)}$ -monotone multifunction with non-empty values. It is shown that the following generalization of the Rockafellar theorem holds. There is a function f: X → ℝ such that Γ is contained in the $Φ^{γ (\cdot, \cdot)}$ -subdifferential of f, $Γ (x) \subset \partial_{Φ}^{γ (\cdot, \cdot)} {f |}_{x}$ .

On the spectral radius in $L_{1} (G)$

E. Porada (1971)

Colloquium Mathematicae

Similarity:

Moufang loops of order coprime to three that cyclically extend groups of dihedral type

Aleš Drápal (2016)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

This paper completely solves the isomorphism problem for Moufang loops $Q = G C$ where $G ⊴ Q$ is a noncommutative group with cyclic subgroup of index two and $| Z (G) | \leq 2$ , $C$ is cyclic, $G \cap C = 1$ , and $Q$ is finite of order coprime to three.

On Peano derivatives in $L^{p} (E_{n})$

S. Lasher (1968)

Studia Mathematica

Similarity:

A note on another construction of graphs with $4 n + 6$ vertices and cyclic automorphism group of order $4 n$

Peteris Daugulis (2017)

Archivum Mathematicum

Similarity:

The problem of finding minimal vertex number of graphs with a given automorphism group is addressed in this article for the case of cyclic groups. This problem was considered earlier by other authors. We give a construction of an undirected graph having $4 n + 6$ vertices and automorphism group cyclic of order $4 n$ , $n \geq 1$ . As a special case we get graphs with $2^{k} + 6$ vertices and cyclic automorphism groups of order $2^{k}$ . It can revive interest in related problems.

Extensions of generic measure-preserving actions

Julien Melleray (2014)

Annales de l’institut Fourier

Similarity:

We show that, whenever $Γ$ is a countable abelian group and $Δ$ is a finitely-generated subgroup of $Γ$ , a generic measure-preserving action of $Δ$ on a standard atomless probability space $(X, μ)$ extends to a free measure-preserving action of $Γ$ on $(X, μ)$ . This extends a result of Ageev, corresponding to the case when $Δ$ is infinite cyclic.

On the index of length four minimal zero-sum sequences

Caixia Shen, Li-meng Xia, Yuanlin Li (2014)

Colloquium Mathematicae

Similarity:

Let G be a finite cyclic group. Every sequence S over G can be written in the form $S = (n ₁ g) \cdot . . . \cdot (n_{l} g)$ where g ∈ G and $n ₁, . . ., n_{l} i \in [1, o r d (g)]$ , and the index ind(S) is defined to be the minimum of $(n ₁ + \dots + n_{l}) / o r d (g)$ over all possible g ∈ G such that ⟨g⟩ = G. A conjecture says that every minimal zero-sum sequence of length 4 over a finite cyclic group G with gcd(|G|,6) = 1 has index 1. This conjecture was confirmed recently for the case when |G| is a product of at most two prime powers. However, the general case is still open. In this paper,...

On Ordinary and Standard Lebesgue Measures on $ℝ^{\infty}$

Gogi Pantsulaia (2009)

Bulletin of the Polish Academy of Sciences. Mathematics

Similarity:

New concepts of Lebesgue measure on $ℝ^{\infty}$ are proposed and some of their realizations in the ZFC theory are given. Also, it is shown that Baker’s both measures [1], [2], Mankiewicz and Preiss-Tišer generators [6] and the measure of [4] are not α-standard Lebesgue measures on $ℝ^{\infty}$ for α = (1,1,...).

Invariant subspaces for operators in a general II1-factor

Uffe Haagerup, Hanne Schultz (2009)

Publications Mathématiques de l'IHÉS

Similarity:

Let ℳ be a von Neumann factor of type II1 with a normalized trace τ. In 1983 L. G. Brown showed that to every operator T∈ℳ one can in a natural way associate a spectral distribution measure μ T (now called the Brown measure of T), which is a probability measure in ℂ with support in the spectrum σ(T) of T. In this paper it is shown that for every T∈ℳ and every Borel set B in ℂ, there is a unique closed T-invariant subspace $𝒦 = 𝒦_{T} (B)$ affiliated with ℳ, such that the Brown measure of ${T |}_{𝒦}$ is concentrated...

Unique Bernoulli $g$ -measures

Anders Johansson, Anders Öberg, Mark Pollicott (2012)

Journal of the European Mathematical Society

Similarity:

We improve and subsume the conditions of Johansson and Öberg and Berbee for uniqueness of a $g$ -measure, i.e., a stationary distribution for chains with complete connections. In addition, we prove that these unique $g$ -measures have Bernoulli natural extensions. We also conclude that we have convergence in the Wasserstein metric of the iterates of the adjoint transfer operator to the $g$ -measure.

Spectral synthesis and operator synthesis

K. Parthasarathy, R. Prakash (2006)

Studia Mathematica

Similarity:

Relations between spectral synthesis in the Fourier algebra A(G) of a compact group G and the concept of operator synthesis due to Arveson have been studied in the literature. For an A(G)-submodule X of VN(G), X-synthesis in A(G) has been introduced by E. Kaniuth and A. Lau and studied recently by the present authors. To any such X we associate a $V^{\infty} (G)$ -submodule X̂ of ℬ(L²(G)) (where $V^{\infty} (G)$ is the weak-* Haagerup tensor product $L^{\infty} (G) \otimes_{w * h} L^{\infty} (G)$ ), define the concept of X̂-operator synthesis and prove that a...

A characterization of Eisenstein polynomials generating extensions of degree $p^{2}$ and cyclic of degree $p^{3}$ over an unramified $𝔭$ -adic field

Maurizio Monge (2014)

Journal de Théorie des Nombres de Bordeaux

Similarity:

Let $p \neq 2$ be a prime. We derive a technique based on local class field theory and on the expansions of certain resultants allowing to recover very easily Lbekkouri’s characterization of Eisenstein polynomials generating cyclic wild extensions of degree $p^{2}$ over $ℚ_{p}$ , and extend it to when the base fields $K$ is an unramified extension of $ℚ_{p}$ . When a polynomial satisfies a subset of such conditions the first unsatisfied condition characterizes the Galois group of the normal closure. We...

A spectral gap theorem in SU $(d)$

Jean Bourgain, Alex Gamburd (2012)

Journal of the European Mathematical Society

Similarity:

We establish the spectral gap property for dense subgroups of SU $(d)$ $(d \geq 2)$ , generated by finitely many elements with algebraic entries; this result was announced in [BG3]. The method of proof differs, in several crucial aspects, from that used in [BG] in the case of SU $(2)$ .

Spectral projections for the twisted Laplacian

Herbert Koch, Fulvio Ricci (2007)

Studia Mathematica

Similarity:

Let n ≥ 1, d = 2n, and let (x,y) ∈ ℝⁿ × ℝⁿ be a generic point in ℝ²ⁿ. The twisted Laplacian $L = - 1 / 2 \sum_{j = 1}^{n} [(\partial_{x_{j}} + i y_{j}) ² + (\partial_{y_{j}} - i x_{j}) ²]$ has the spectrum n + 2k = λ²: k a nonnegative integer. Let $P_{λ}$ be the spectral projection onto the (infinite-dimensional) eigenspace. We find the optimal exponent ϱ(p) in the estimate $| | P_{λ} {u | |}_{L^{p} (ℝ^{d})} ≲ λ^{ϱ (p)} {| | u | |}_{L ² (ℝ^{d})}$ for all p ∈ [2,∞], improving previous partial results by Ratnakumar, Rawat and Thangavelu, and by Stempak and Zienkiewicz. The expression for ϱ(p) is ϱ(p) = 1/p -1/2 if 2 ≤ p ≤ 2(d+1)/(d-1), ϱ(p) = (d-2)/2 - d/p...