Characterizations of Banach Spaces which are not Isomorphic to any of their Proper Subspaces
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Qingping Zeng
und
Huaijie Zhong
Abstract
In this note we obtain some characterizations of Banach spaces which are not isomorphic to any of their proper subspaces. In particular, we show that a Banach space X is not isomorphic to any of its proper subspaces if and only the equality σRD(LT) = σLD(T) holds for every bounded linear operator T on X if and only if int(σ(T)) ⊆ σLD(T) holds for every bounded linear operator T on X, where LT denotes the left multiplication operator by T.
References
[1] AIENA, P.: Fredholm and Local Spectral Theory, with Application to Multipliers, Kluwer Academic Publishers, Dordrecht, 2004.Suche in Google Scholar
[2] AIENA, P.: Quasi-Fredholm operators and localized SVEP, Acta Sci. Math. (Szeged) 73 (2007), 251-263.Suche in Google Scholar
[3] AIENA, P.-BIONDI, M. T.-CARPINTERO, C.: On Drazin invertibility, Proc. Amer. Math. Soc. 136 (2008), 2839-2848.10.1090/S0002-9939-08-09138-7Suche in Google Scholar
[4] AIENA, P.-MILLER, T. L.: On generalized a-Browder’s theorem, Studia Math. 180 (2007), 285-300.10.4064/sm180-3-7Suche in Google Scholar
[5] AIENA, P.-SANABRIA, J. E.: On left and right poles of the resolvent, Acta Sci. Math. (Szeged) 74 (2008), 667-685.Suche in Google Scholar
[6] BEL HADJ FREDJ, O.-BURGOS,M.-OUDGHIRI,M.: Ascent spectrum and essential ascent spectrum, Studia Math. 187 (2008), 59-73.10.4064/sm187-1-3Suche in Google Scholar
[7] BERKANI,M.: Restrition of operator to the range of its power, Studia Math. 140 (2000), 163-175.10.4064/sm-140-2-163-175Suche in Google Scholar
[8] BERKANI, M.-KOLIHA, J. J.: Weyl type theorems for bounded linear operators, Acta Sci. Math. (Szeged) 69 (2003), 359-376.Suche in Google Scholar
[9] BERKANI,M.-SARIH, M.: An Atkinson-type theorem for B-Fredholm operators, Studia Math. 148 (2001), 251-257.10.4064/sm148-3-4Suche in Google Scholar
[10] BOASSO, E.: Drazin spectra of Banach space operators and Banach algebra elements, J. Math. Anal. Appl. 359 (2009), 48-55.10.1016/j.jmaa.2009.05.036Suche in Google Scholar
[11] BURGOS, M. ET AL: The descent spectrum and perturbations, J. Operator Theory 56 (2006), 259-271.Suche in Google Scholar
[12] GOWERS, W. T.: A solution to Banach’s hyperplane problem, Bull. Lond. Math. Soc. 26 (1994), 523-530. 13] GOWERS, W. T.-MAUREY, B.: The unconditional basic sequence problem, J. Amer. Math. Soc. 6 (1993), 851-874.10.1090/S0894-0347-1993-1201238-0Suche in Google Scholar
[14] GRABINER, S.: Uniform ascent and descent of bounded operators, J. Math. Soc. Japan 34 (1982), 317-337.10.2969/jmsj/03420317Suche in Google Scholar
[15] HAÏLY, A.-KAIDI, A.-RODRÍGUEZS PALACIOS, A.: Algebra descent spectrum of operators, Israel J. Math. 177 (2010), 349-368.10.1007/s11856-010-0050-9Suche in Google Scholar
[16] LAUSTSEN, N. J.: On ring-theoretic (in)finiteness of Banach algebras of operators on Banach spaces, Glasg. Math. J. 45 (2003), 11-19.10.1017/S0017089502008947Suche in Google Scholar
[17] MBEKHTA, M.-MÜLLER, V.: On the axiomatic theory of spectrum II, Studia Math. 119 (1996), 129-147.10.4064/sm-119-2-129-147Suche in Google Scholar
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Artikel in diesem Heft
- The M-Regular Graph of a Commutative Ring
- Further Properties of the Lattice of Torsion Classes of Abelian Cyclically Ordered Groups
- Free Power-Commutative Groupoids
- On Systems of Independent Sets
- Note on G-Module Structure of Orders
- Semisimple Hopf Algebras of Dimension 2q3
- On the Convergence of a Mapped by a Function
- Multiple Solutions of Nonlinear Fractional Differential Equations with p-Laplacian Operator and Nonlinear Boundary Conditions
- Meromorphic Functions Sharing Pairs of Small Functions
- Sharp Inequalities for Polygamma Functions
- Existence Results for Some Higher-Order Evolution Equations with Time-Dependent Unbounded Operator Coefficients
- Existence of Ground State Solutions for Hamiltonian Elliptic Systems with Gradient Terms
- Approximate Higher Ring Derivations in Non-Archimedean Banach Algebras
- Characterizations of Banach Spaces which are not Isomorphic to any of their Proper Subspaces
- Operator Inequalities Related to Q-Class Functions
- On a Class of Locally Dually Flat (α,β)–Metrics
- Limit Theorems for the Counting Function of Eigenvalues up to Edge in Covariance Matrices
- A Generalization of Jakubec's Formula
