Displaying similar documents to “Cyclic vectors and invariant subspaces for the backward shift operator”

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 ) | ≥ 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....

Uniformly cyclic vectors

Joseph Rosenblatt (2006)

Colloquium Mathematicae

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A group acting on a measure space (X,β,λ) may or may not admit a cyclic vector in L ∞ ( X ) . This can occur when the acting group is as big as the group of all measure-preserving transformations. But it does not occur, even though there is no cardinality obstruction to it, for the regular action of a group on itself. The connection of cyclic vectors to the uniqueness of invariant means is also discussed.

Subnormal operators, cyclic vectors and reductivity

Béla Nagy (2013)

Studia Mathematica

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Two characterizations of the reductivity of a cyclic normal operator in Hilbert space are proved: the equality of the sets of cyclic and *-cyclic vectors, and the equality L²(μ) = P²(μ) for every measure μ equivalent to the scalar-valued spectral measure of the operator. A cyclic subnormal operator is reductive if and only if the first condition is satisfied. Several consequences are also presented.

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 ∞ be a sequence of positive numbers and 1 ≤ p < ∞ . We consider the space H p ( β ) of all power series f ( z ) = ∑ n = 0 ∞ f ^ ( n ) z n such that ∑ n = 0 ∞ | f ^ ( n ) | p β ( n ) p < ∞ . We investigate strict cyclicity of H p ∞ ( 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 ∞ ( β ) . We also give a necessary condition for a composition operator to be bounded on H p ( β ) when H p ∞ ( β ) is strictly cyclic.

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 ) ≤ 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...