Hermitian operators on $H^{∞}_E$ and $S^{∞}_{}$

James Jamison

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On operators from $ℓ_{s}$ to $ℓ_{p} \otimes ̂ ℓ_{q}$ or to $ℓ_{p} \hat{\otimes ̂} ℓ_{q}$

Christian Samuel (2010)

Colloquium Mathematicae

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We show that every operator from $ℓ_{s}$ to $ℓ_{p} \otimes ̂ ℓ_{q}$ is compact when 1 ≤ p,q < s and that every operator from $ℓ_{s}$ to $ℓ_{p} \hat{\otimes ̂} ℓ_{q}$ is compact when 1/p + 1/q > 1 + 1/s.

2-summing multiplication operators

Dumitru Popa (2013)

Studia Mathematica

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Let 1 ≤ p < ∞, $= {(X ₙ)}_{n \in ℕ}$ be a sequence of Banach spaces and $l_{p} ()$ the coresponding vector valued sequence space. Let $= {(X ₙ)}_{n \in ℕ}$ , $= {(Y ₙ)}_{n \in ℕ}$ be two sequences of Banach spaces, $= {(V ₙ)}_{n \in ℕ}$ , Vₙ: Xₙ → Yₙ, a sequence of bounded linear operators and 1 ≤ p,q < ∞. We define the multiplication operator $M_{} : l_{p} () \to l_{q} ()$ by $M_{} ({(x ₙ)}_{n \in ℕ}) : = {(V ₙ (x ₙ))}_{n \in ℕ}$ . We give necessary and sufficient conditions for $M_{}$ to be 2-summing when (p,q) is one of the couples (1,2), (2,1), (2,2), (1,1), (p,1), (p,2), (2,p), (1,p), (p,q); in the last case 1 < p < 2, 1 < q < ∞. ...

Linear maps preserving $A$ -unitary operators

Abdellatif Chahbi, Samir Kabbaj, Ahmed Charifi (2016)

Mathematica Bohemica

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Let $ℋ$ be a complex Hilbert space, $A$ a positive operator with closed range in $ℬ (ℋ)$ and $ℬ_{A} (ℋ)$ the sub-algebra of $ℬ (ℋ)$ of all $A$ -self-adjoint operators. Assume $φ : ℬ_{A} (ℋ)$ onto itself is a linear continuous map. This paper shows that if $φ$ preserves $A$ -unitary operators such that $φ (I) = P$ then $ψ$ defined by $ψ (T) = P φ (P T)$ is a homomorphism or an anti-homomorphism and $ψ (T^{♯}) = ψ {(T)}^{♯}$ for all $T \in ℬ_{A} (ℋ)$ , where $P = A^{+} A$ and $A^{+}$ is the Moore-Penrose inverse of $A$ . A similar result is also true if $φ$ preserves $A$ -quasi-unitary operators in both directions such that there...

On the equation $ϕ (x + m) = ϕ (x) + m$

A. Makowski (1964)

Matematički Vesnik

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On C $^{*}$ -spaces

P. Srivastava, K. K. Azad (1981)

Matematički Vesnik

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$ℵ_{1}$ -incompactness of Z

Ralph McKenzie (1971)

Colloquium Mathematicae

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On a characterization of $L^{p}$ -norm

Janusz Matkowski (1989)

Annales Polonici Mathematici

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On the $p^{λ}$ problem

Stephan Baier (2004)

Acta Arithmetica

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The existence of $P (α)$ -points of N* for $ℵ_{0} α < 𝔠$

A. Szymański (1977)

Colloquium Mathematicae

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A characterization of the disc $D^{n}$

Th. Friedrich (1974)

Colloquium Mathematicae

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Perturbations of real parts of eigenvalues of bounded linear operators in a Hilbert space

Michael Gil' (2024)

Czechoslovak Mathematical Journal

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Let $A$ be a bounded linear operator in a complex separable Hilbert space $ℋ$ , and $S$ be a selfadjoint operator in $ℋ$ . Assuming that $A - S$ belongs to the Schatten-von Neumann ideal $𝒮_{p}$ $(p > 1),$ we derive a bound for $\sum_{k} {| R λ_{k} (A) - λ_{k} (S) |}^{p}$ , where $λ_{k} (A)$ $(k = 1, 2, \dots)$ are the eigenvalues of $A$ . Our results are formulated in terms of the “extended” eigenvalue sets in the sense introduced by T. Kato. In addition, in the case $p = 2$ we refine the Weyl inequality between the real parts of the eigenvalues of $A$ and the eigenvalues...

An application of the method wherein the $p h i$ - and $c h i$ - methods are combined for the determination of the grating constant. [II.]

Swami Jnanananda (1936)

Časopis pro pěstování matematiky a fysiky

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On the proximate order of $f^{(s)} (z) * g^{(s)} (z)$ and ${[f (z) * g (z)]}^{(s)}$

M. K. Sen (1971)

Annales Polonici Mathematici

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Геометрическая теория состояний, граница фон Неймана, двойственность $C^{*}$ -алгерб

А.М. Вершик (1972)

Zapiski naucnych seminarov Leningradskogo

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On spirallike functions of order $α$ and type $β$ with fixed second coefficient

M. K. Aouf (1988)

Matematički Vesnik

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Addendum to “On the $p^{λ}$ problem”

Stephan Baier (2005)

Acta Arithmetica

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Multiplication operators on $L (L_{p})$ and $ℓ_{p}$ -strictly singular operators

William Johnson, Gideon Schechtman (2008)

Journal of the European Mathematical Society

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A classification of weakly compact multiplication operators on $L (L_{p}),$ 1<p< $, i s g i v e n . T h i s a n s w e r s a q u e s t i o n r a i s e d b y S a k s m a n a n d T y l l i i n 1992 . T h e c l a s s i f i c a t i o n i n v o l v e s t h e c o n c e p t o f$ p $- s t r i c t l y s i n g u l a r o p e r a t o r s, a n d w e a l s o i n v e s t i g a t e t h e s t r u c t u r e o f g e n e r a l$ p $- s t r i c t l y s i n g u l a r o p e r a t o r s o n$ Lp $. T h e m a i n r e s u l t i s t h a t i f a n o p e r a t o r$ T $o n$ Lp $,$ 1<p<2 $, i s$ p $- s t r i c t l y s i n g u l a r a n d$ T|X $i s a n i s o m o r p h i s m f o r s o m e s u b s p a c e$ X $o f$ Lp $, t h e n$ X $e m b e d s i n t o$ Lr $f o r a l l$ r<2 $, b u t$ X $n e e d n o t b e i s o m o r p h i c t o a H i l b e r t s p a c e .$ It is also shown that if $T$ is convolution by a biased coin on $L_{p}$ of the Cantor group, $1 \leq p < 2$ , and $T_{| X}$ is an isomorphism for some reflexive subspace $X$ of $L_{p}$ , then $X$ is isomorphic to a Hilbert space. The case $p = 1$ answers a question asked by Rosenthal in 1976.

The general methods of finding the sum $S_{n}$ for all kinds of series, II

K. Orlov (1981)

Matematički Vesnik

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Displaying similar documents to “Hermitian operators on H E ∞ and S ∞ ”

Displaying similar documents to “Hermitian operators on $H_{E}^{\infty}$ and $S_{}^{\infty}$ ”