Results 171 to 180 of about 66,942 (205)

Partial Integral Operators on Banach–Kantorovich Spaces

Mathematical Notes, 2023
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Arziev, A. D., Kudaybergenov, K. K., Orinbaev, P. R., Tangirbergen, A. K.   +3 more
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Superstable operators on Banach spaces

Israel Journal of Mathematics, 1993
The paper is devoted to study the spectrum of bounded linear operators on Banach spaces. The main result given in Theorem 3.7 is that the spectrum of a power bounded linear operator on a superreflexive Banach space, situated on the unit circle, is countable if and only if this operator is superstable. The latter notion is introduced by using ultrapower
Nagel, Rainer, Räbiger, Frank
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Compact Operators on Banach Spaces

2001
In this chapter, we present some basic properties of compact operators in L(X, Y), where X and Y are Banach spaces. The results enable us to determine conditions under which certain integral equations have solutions in L p ([a, b]), 1 < p < ∞ or C([a, b]).
Marián Fabian, Petr Habala, Petr Hájek, Vicente Montesinos Santalucía, Jan Pelant, Václav Zizler   +5 more
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k-BICOMPOUND OPERATORS ON BANACH SPACES

International Journal of Functional Analysis, Operator Theory and Applications, 2018
Summary: In this paper, we define and study a new class of operators on Banach spaces which is called \(k\)-bicompound operators. We use these operators to give a partial answer to two open problems in the literature (cf. [\textit{N. Bamerni} and \textit{A. Kiliçman}, Carpathian Math. Publ. 8, No. 1, 3--10 (2016; Zbl 1350.47005); \textit{N. Bamerni}, ``
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On irreducible operator*-algebras on Banach spaces

Acta Mathematica Hungarica, 1984
Let L(X) be the algebra of all bounded linear operators on a Banach space X. A subalgebra \({\mathcal B}\subset L(X)\) is called irreducible if for each pair x,\(y\in X\), \(x\neq 0\) there exists \(A\in {\mathcal B}\) such that \(Ax=y.\) A subalgebra \({\mathcal B}\subset L(X)\) is called strongly irreducible if for each \(y\in X\) there exists a ...
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Compact Operators on Banach Spaces

2010
In this chapter we study basic properties of compact operators on Banach spaces. We present the elementary spectral theory of compact operators in Banach spaces, including the spectral radius and properties of eigenvalues. Then we discus basic spectral properties of selfadjoint operators on Hilbert spaces, their spectral decomposition, and show some of
Marián Fabian, Petr Habala, Petr Hájek, Vicente Montesinos, Václav Zizler   +4 more
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Normal operators on Banach spaces

Glasgow Mathematical Journal, 1979
A (bounded, linear) operator H on a Banach space is said to be hermitian if ∥exp(itH)∥ = 1 for all real t. An operator N on is said to be normal if N = H + iK, where H and K are commuting hermitian operators. These definitions generalize those familiar concepts of operators on Hilbert spaces.
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Linear Operators on Banach Spaces

2013
Let \((\mathcal{X},\|\cdot \|)\) and \((\mathcal{Y},\|\cdot \|_{1})\) be two Banach spaces over the same field \(\mathbb{F}\). A mapping \(A: D(A) \subset \mathcal{X} \rightarrow \mathcal{Y}\) satisfying $$\displaystyle{A(\alpha x +\beta y) =\alpha Ax +\beta Ay}$$ for all x,y∈D(A) and \(\alpha,\beta \in \mathbb{F}\), is called a linear operator ...
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The bounded additive operation on Banach space

Proceedings of the American Mathematical Society, 1951
In his book on the theory of linear operations (p. 54) Banach proves that an additive operation U on a normed linear space to another is continuous (hence, linear, at least for real spaces) if and only if it satisfies the Lipschitz condition I U(x) I
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Commutators of operators on Banach spaces

2002
In the paper under review, one investigates Banach space versions of the fact that every bounded linear operator on a complex infinite-dimensional Hilbert space is the sum of two commutators. Thus, one finds out that the same fact holds when the Hilbert space is replaced by one of the Banach spaces \(c_0\), \(C([0,1])\), \(\ell_p\) or \(L_p([0,1 ...
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