On full and nearly full operators in complex Banach spaces
Abstract
A bounded linear operator $T$ on a complex Banach space $\mathcal{X}$ is said to be full if $\overline{T\mathcal{M}}=\mathcal{M}$ for every invariant subspace $\mathcal{M}$ of $\mathcal{X}$. It is nearly full if $\overline{T\mathcal{M}}$ has finite codimension in $\mathcal{M}$. In this paper, we focus our attention to characterize full and nearly full operators in complex Banach spaces, showing that some valid results in complex Hilbert spaces can be generalized to this context.
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References
F. Bonsal, J. Duncan, Numerical Ranges of Operators on Normed Spaces and of Elements of Normed Algebras, London Math. Soc. Lecture Note Series No 2, Cambridge University Press (1971). DOI: https://doi.org/10.1017/CBO9781107359895
F. Bonsal, J. Duncan, Numerical Ranges II, London Math. Soc. Lecture Note Series No 10. Cambridge University Press (1973).
J. Bravo, Relations between latT, latT −1 , latT 2 and operators with compact imaginary parts, Ph. D. Dissertation. University of California Berkeley (1980).
J. Bravo, Operadores Regulares en Alglat (T) ∩ {T} ′ , Notas del Departamento de Matematicas. Facultad Experimental de Ciencias. LUZ (2007).
H. R. Dowson, Spectral Theory of Linear Operator, Academic Press (1978).
J. Erdos, Dissipative operators and approximation of inverse, Bull London Math. Soc. 11 , 142-144, (1979). DOI: https://doi.org/10.1112/blms/11.2.142
J. Erdos, Singly generated algebras containing compact operators, J. of Operator Theory. 2, 211-214, (1979).
A. Feintuch, On invertible operators and invariant subspaces, Proc. Amer. Math. Soc. 43, 123-126, (1974). DOI: https://doi.org/10.1090/S0002-9939-1974-0331082-8
A. Feintuch, On algebras generated by invertible operators, Proc. Amer. Math. Soc. 63, 66-68, (1977). DOI: https://doi.org/10.1090/S0002-9939-1977-0435929-9
A. Feintuch, On polynomial approximation of the inverse of an operator, J. Linear Algebra and its Applications. 389, 323-328, (2004). DOI: https://doi.org/10.1016/j.laa.2004.04.004
P. R. Halmos, Introduction to Hilbert Space, 2nd ed. Chelsea-New York (1957).
S. Karanasios, Full operators and approximation of inverses, J. London Math. Soc. 30, 295-304, (1984). DOI: https://doi.org/10.1112/jlms/s2-30.2.295
S. Karanasios, Full operators on reflexive complex Banach spaces, Bull. Greek Math. Soc. 36, 81-86, (1994).
S. Karanasios, D. Pappas, Approximability of the Generalized Inverse of an Operator, Journal Inst. Math. & Comp. Sci. 19(1), 73-77, (2006).
L. Ortu˜nez, Tesis de Maestria del PEAM (LUZ), Maracaibo (1984).
W. R. Pacheco, Full operators and algebras generated by invertible operators, Extracta Math. 24(3), 259-264, (2009).
H. Radjavi, P. Rosenthal, Invariant Subspaces, Springer-Verlag (1974). DOI: https://doi.org/10.1007/978-3-642-65574-6
H. Radjavi, P. Rosenthal, Invariant Subspaces, Courier Corporation (2003).
N.K. Nikolskii, Treatise on the Shift Operator, Springer, Berlin 1986. DOI: https://doi.org/10.1007/978-3-642-70151-1
E. Rosales, Tesis Doctoral, Universidad del Zulia (2010).
D. Sarason, The Hp Spaces of an Annulus, Mem. Amer. Math. Soc. 56, (1965). DOI: https://doi.org/10.1090/memo/0056
A. E. Taylor, Introduction to Functional Analysis, New York, John Wiley and Sons (1958).
J. Wermer, On invariant subspaces of normal operators, Proc. Amer. Math.Soc. 3, 270-277, (1952). DOI: https://doi.org/10.1090/S0002-9939-1952-0048700-X
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