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1
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Bidual Spaces and Reflexivity of Real Normed Spaces

100%
Narita K., Endou N., Shidama Y.
Formalized Mathematics
|
2014
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tom 22
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nr 4
303-311
EN
In this article, we considered bidual spaces and reflexivity of real normed spaces. At first we proved some corollaries applying Hahn-Banach theorem and showed related theorems. In the second section, we proved the norm of dual spaces and defined the natural mapping, from real normed spaces to bidual spaces. We also proved some properties of this mapping. Next, we defined real normed space of R, real number spaces as real normed spaces and proved related theorems. We can regard linear functionals as linear operators by this definition. Accordingly we proved Uniform Boundedness Theorem for linear functionals using the theorem (5) from [21]. Finally, we defined reflexivity of real normed spaces and proved some theorems about isomorphism of linear operators. Using them, we proved some properties about reflexivity. These formalizations are based on [19], [20], [8] and [1].
2
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Operators preserving ideals in C*-algebras

100%
S. Shul'Man V.
Studia Mathematica
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1994
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tom 109
|
nr 1
67-72
EN
The aim of this paper is to prove that derivations of a C*-algebra A can be characterized in the space of all linear continuous operators T : A → A by the conditions T(1) = 0, T(L∩R) ⊂ L + R for any closed left ideal L and right ideal R. As a corollary we get an extension of the result of Kadison [5] on local derivations in W*-algebras. Stronger results of this kind are proved under some additional conditions on the cohomologies of A.
3
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A quasinilpotent operator with reflexive commutant

100%
Zając M.
Studia Mathematica
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1996
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tom 118
|
nr 3
277-283
EN
An example of a nonzero quasinilpotent operator with reflexive commutant is presented.
4
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The set of automorphisms of B(H) is topologically reflexive in B(B(H))

100%
Molnár L.
Studia Mathematica
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1997
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tom 122
|
nr 2
183-193
EN
The aim of this paper is to prove the statement announced in the title which can be reformulated in the following way. Let H be a separable infinite-dimensional Hilbert space and let Φ: B(H) → B(H) be a continuous linear mapping with the property that for every A ∈ B(H) there exists a sequence $(Φ_n)$ of automorphisms of B(H) (depending on A) such that $Φ(A)= lim_n Φ_n(A)$. Then Φ is an automorphism. Moreover, a similar statement holds for the set of all surjective isometries of B(H).
5
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A quasi-nilpotent operator with reflexive commutant, II

100%
Müller V., Zając M.
Studia Mathematica
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1999
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tom 132
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nr 2
173-177
EN
A new example of a non-zero quasi-nilpotent operator T with reflexive commutant is presented. The norms $|T^n|$ converge to zero arbitrarily fast.
6
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Uniformly non-\(l_n^1\) Besicovitch-Orlicz space of almost periodic functions

88%
Morsli M., Boulahia F.
Commentationes Mathematicae
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2005
|
tom 45
|
nr 1
EN
We consider uniformly non-\(l_n^1\) almost periodic functions. It is shown that this property is equivalent to the reflexivity of this space.
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