Stability of Almost Closed Operators on a Hilbert Space
DOI:
https://doi.org/10.5644/SJM.05.1.12Keywords:
Closed operators, almost closed operators, sum, product, limits and adjointAbstract
We introduce the notion of almost closed linear operators acting in a Hilbert space. This class of operators contains the set of all closed linear operators and is invariant under addition, composition and limits.
2000 Mathematics Subject Classification. 47A05, 47B33
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References
S. R. Caradus, Semiclosed operators, Pacific J. Math., 44 (1) (1973), 75–79.
P. R. Chernoff, A semibounded closed symmetric operator whose square has trivial domain, Proc. Amer. Math. Soc., 89 (1983), 289–290.
R. W. Cross, On the continuous linear image of a Banach space, J. Aust. Math. Soc. Ser. A, 29 (2) (1980), 219–234.
J. Dixmier, L’adjoint du produit de deux op´erateurs ferm ´es, Ann. Fac. Sci. Univ. Toulouse, 4`emes´e rie, 11 (1974), 101–106.
M. R. Embry, Factorization of operators on Banach spaces, Proc. Amer. Math. Soc., 38 (1973), 587–590.
P. A. Fillmore and J. P. Williams, On operator ranges, Adv. Math. 7 (1971), 254–281.
E. Hille and R. S. Philips, Functional Analysis and Semi-Groups, Amer. Math. Soc., Providence, Rhode Island, 1957.
T. Kato, Perturbation Theory for Linear Operators, 2nd edition, Springer, 1980.
B. Messirdi, M. H. Mortad, A. Azzouz and G. Djellouli, A topological characterization of the product of two closed operators, Colloq. Math., 112 (2) (2008), 269–278.
B. Messirdi and M. H. Mortad, On different products of closed operators, Banach J. Math. Anal., 2 (1) (2008), 40–47.
M. Reed and B. Simon, Methods of Modern Mathematical Physics, Vol. 1, Functional Analysis, Vol. 2, Fourier Analysis, Self-adjointness, Academic Press, 1978.
W. Rudin, Functional Analysis, Mc Graw Hill, 1973.
L. Schwartz, Th´eorie des distributions, Editions Hermann, 1973.
