Uniformly cyclic vectors

Joseph Rosenblatt

Displaying similar documents to “Uniformly cyclic vectors”

Subnormality and cyclicity

Franciszek Hugon Szafraniec (2005)

Banach Center Publications

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For an unbounded operator S the question whether its subnormality can be built up from that of every $S_{f}$ , the restriction of S to a cyclic space generated by f in the domain of S, is analyzed. Though the question at large has been left open some partial results are presented and a possible way to prove it is suggested as well.

Cyclic vectors and invariant subspaces for the backward shift operator

R. G. Douglas, H. S. Shapiro, A. L. Shields (1970)

Annales de l'institut Fourier

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The operator $U$ of multiplication by $z$ on the Hardy space $H^{2}$ of square summable power series has been studied by many authors. In this paper we make a similar study of the adjoint operator $U^{*}$ (the “backward shift”). Let $K_{f}$ denote the cyclic subspace generated by $f (f \in H^{2})$ , that is, the smallest closed subspace of $H^{2}$ that contains ${U^{* n} f}$ $(n \geq 0)$ . If $K_{f} = H^{2}$ , then $f$ is called a cyclic vector for $U^{*}$ . Theorem : $f$ is a cyclic vector if and only if there is a function $g$ , meromorphic and of bounded Nevanlinna...

Linear and cyclic radio k-labelings of trees

Mustapha Kchikech, Riadh Khennoufa, Olivier Togni (2007)

Discussiones Mathematicae Graph Theory

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Motivated by problems in radio channel assignments, we consider radio k-labelings of graphs. For a connected graph G and an integer k ≥ 1, a linear radio k-labeling of G is an assignment f of nonnegative integers to the vertices of G such that $| f (x) - f (y) | \geq k + 1 - d_{G} (x, y)$ , for any two distinct vertices x and y, where $d_{G} (x, y)$ is the distance between x and y in G. A cyclic k-labeling of G is defined analogously by using the cyclic metric on the labels. In both cases, we are interested in minimizing the span of the labeling....

A note on cyclic chromatic number

Jana Zlámalová (2010)

Discussiones Mathematicae Graph Theory

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A cyclic colouring of a graph G embedded in a surface is a vertex colouring of G in which any two distinct vertices sharing a face receive distinct colours. The cyclic chromatic number $χ_{c} (G)$ of G is the smallest number of colours in a cyclic colouring of G. Plummer and Toft in 1987 conjectured that $χ_{c} (G) \leq Δ * + 2$ for any 3-connected plane graph G with maximum face degree Δ*. It is known that the conjecture holds true for Δ* ≤ 4 and Δ* ≥ 18. The validity of the conjecture is proved in the paper for some...

Strictly cyclic algebra of operators acting on Banach spaces $H^{p} (β)$

Bahmann Yousefi (2004)

Czechoslovak Mathematical Journal

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Let ${β (n)}_{n = 0}^{\infty}$ be a sequence of positive numbers and $1 \leq p < \infty$ . We consider the space $H^{p} (β)$ of all power series $f (z) = \sum_{n = 0}^{\infty} \hat{f} (n) z^{n}$ such that $\sum_{n = 0}^{\infty} {| \hat{f} (n) |}^{p} β {(n)}^{p} < \infty$ . We investigate strict cyclicity of $H_{p}^{\infty} (β)$ , the weakly closed algebra generated by the operator of multiplication by $z$ acting on $H^{p} (β)$ , and determine the maximal ideal space, the dual space and the reflexivity of the algebra $H_{p}^{\infty} (β)$ . We also give a necessary condition for a composition operator to be bounded on $H^{p} (β)$ when $H_{p}^{\infty} (β)$ is strictly cyclic.

Cyclic and dihedral constructions of even order

Aleš Drápal (2003)

Commentationes Mathematicae Universitatis Carolinae

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Let $G (\circ)$ and $G (*)$ be two groups of finite order $n$ , and suppose that they share a normal subgroup $S$ such that $u \circ v = u * v$ if $u \in S$ or $v \in S$ . Cases when $G / S$ is cyclic or dihedral and when $u \circ v \neq u * v$ for exactly $n^{2} / 4$ pairs $(u, v) \in G \times G$ have been shown to be of crucial importance when studying pairs of 2-groups with the latter property. In such cases one can describe two general constructions how to get all possible $G (*)$ from a given $G = G (\circ)$ . The constructions, denoted by $G [α, h]$ and $G [β, γ, h]$ , respectively, depend on a coset $α$ (or two cosets $β$ and $γ$ ) modulo...

Note on cyclic decompositions of complete bipartite graphs into cubes

Dalibor Fronček (1999)

Discussiones Mathematicae Graph Theory

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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.

Piecewise convex transformations with no finite invariant measure

Tomasz Komorowski (1991)

Annales Polonici Mathematici

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Abstract. The paper concerns the problem of the existence of a finite invariant absolutely continuous measure for piecewise $C^{2}$ -regular and convex transformations T: [0, l]→[0,1]. We show that in the case when T’(0) = 1 and T"(0) exists T does not admit such a measure. This result is complementary to the ones contained in [3] and [5].

Bounded point evaluations for multicyclic operators

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

Banach Center Publications

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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...

Circles passing through five or more integer points

Shaunna M. Plunkett-Levin (2013)

Acta Arithmetica

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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...