Displaying similar documents to “On complete-cocomplete subspaces of an inner product space”

Extensions of linear operators from hyperplanes of l ∞ ( n )

Marco Baronti, Vito Fragnelli, Grzegorz Lewicki (1995)

Commentationes Mathematicae Universitatis Carolinae

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Let Y ⊂ l ∞ ( n ) be a hyperplane and let A ∈ ℒ ( Y ) be given. Denote 𝒜 = { L ∈ ℒ ( l ∞ ( n ) , Y ) : L ∣ Y = A } and λ A = inf { ∥ L ∥ : L ∈ 𝒜 } . In this paper the problem of calculating of the constant λ A is studied. We present a complete characterization of those A ∈ ℒ ( Y ) for which λ A = ∥ A ∥ . Next we consider the case λ A > ∥ A ∥ . Finally some computer examples will be presented.

Determinants of matrices associated with incidence functions on posets

Shaofang Hong, Qi Sun (2004)

Czechoslovak Mathematical Journal

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Let S = { x 1 , ⋯ , x n } be a finite subset of a partially ordered set P . Let f be an incidence function of P . Let [ f ( x i ∧ x j ) ] denote the n × n matrix having f evaluated at the meet x i ∧ x j of x i and x j as its i , j -entry and [ f ( x i ∨ x j ) ] denote the n × n matrix having f evaluated at the join x i ∨ x j of x i and x j as its i , j -entry. The set S is said to be meet-closed if x i ∧ x j ∈ S for all 1 ≤ i , j ≤ n . In this paper we get explicit combinatorial formulas for the determinants of matrices [ f ( x i ∧ x j ) ] and [ f ( x i ∨ x j ) ] on any meet-closed set S . We also obtain necessary and sufficient conditions for...

On Meager Additive and Null Additive Sets in the Cantor Space 2 ω and in ℝ

Tomasz Weiss (2009)

Bulletin of the Polish Academy of Sciences. Mathematics

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Let T be the standard Cantor-Lebesgue function that maps the Cantor space 2 ω onto the unit interval ⟨0,1⟩. We prove within ZFC that for every X ⊆ 2 ω , X is meager additive in 2 ω iff T(X) is meager additive in ⟨0,1⟩. As a consequence, we deduce that the cartesian product of meager additive sets in ℝ remains meager additive in ℝ × ℝ. In this note, we also study the relationship between null additive sets in 2 ω and ℝ.

A note on radio antipodal colourings of paths

Riadh Khennoufa, Olivier Togni (2005)

Mathematica Bohemica

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The radio antipodal number of a graph G is the smallest integer c such that there exists an assignment f V ( G ) → { 1 , 2 , ... , c } satisfying | f ( u ) - f ( v ) | ≥ D - d ( u , v ) for every two distinct vertices u and v of G , where D is the diameter of G . In this note we determine the exact value of the antipodal number of the path, thus answering the conjecture given in [G. Chartrand, D. Erwin and P. Zhang, Math. Bohem. 127 (2002), 57–69]. We also show the connections between this colouring and radio labelings.