Displaying similar documents to “A characterization of the B -realcompact space”

On the complemented subspaces of the Schreier spaces

I. Gasparis, D. Leung (2000)

Studia Mathematica

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It is shown that for every 1 ≤ ξ < ω, two subspaces of the Schreier space X ξ generated by subsequences ( e l n ξ ) and ( e m n ξ ) , respectively, of the natural Schauder basis ( e n ξ ) of X ξ are isomorphic if and only if ( e l n ξ ) and ( e m n ξ ) are equivalent. Further, X ξ admits a continuum of mutually incomparable complemented subspaces spanned by subsequences of ( e n ξ ) . It is also shown that there exists a complemented subspace spanned by a block basis of ( e n ξ ) , which is not isomorphic to a subspace generated by a subsequence of ( e n ζ ) ,...

On some singular integral operatorsclose to the Hilbert transform

T. Godoy, L. Saal, M. Urciuolo (1997)

Colloquium Mathematicae

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Let m: ℝ → ℝ be a function of bounded variation. We prove the L p ( ) -boundedness, 1 < p < ∞, of the one-dimensional integral operator defined by T m f ( x ) = p . v . k ( x - y ) m ( x + y ) f ( y ) d y where k ( x ) = j 2 j φ j ( 2 j x ) for a family of functions φ j j satisfying conditions (1.1)-(1.3) given below.

On a function that realizes the maximal spectral type

Krzysztof Frączek (1997)

Studia Mathematica

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We show that for a unitary operator U on L 2 ( X , μ ) , where X is a compact manifold of class C r , r , ω , and μ is a finite Borel measure on X, there exists a C r function that realizes the maximal spectral type of U.

Isomorphism of certain weak L p spaces

Denny Leung (1993)

Studia Mathematica

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It is shown that the weak L p spaces p , , L p , [ 0 , 1 ] , and L p , [ 0 , ) are isomorphic as Banach spaces.