A note on range-kernel uncomplementation

• Autorzy: Kubrusly C. , Duggal B. P.

Identyfikatory

DOI

10.1515/dema-2017-0027

• Języki publikacji: EN

Abstrakty

EN

This note exhibits a Banach-space operator such that neither the range nor the kernel is complemented both for the operator and its adjoint.

Słowa kluczowe

EN

Banach-space operators; complementation; closed range; Fredholm operator

PL

przestrzeń Banacha; operator Banacha; uzupełnienie; zasięg zamknięty; operator Fredholma

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2017
• Tom: Vol. 50, nr 1
• Strony: 252--260
• Opis fizyczny: Bibliogr. 16 poz.

Twórcy

autor

Kubrusly C.

• Catholic University of Rio de Janeiro, 22453-900, Rio de Janeiro, RJ, Brazil

autor

Duggal B. P.

• 8 Redwood Grove, Northfield Avenue, Ealing, London W5 4SZ, United Kingdom

Bibliografia

• [1] Kubrusly C. S., Duggal B. P., Upper-lower and left-right semi-Fredholmness, Bull. Belg. Math. Soc. Simon Stevin, 2016, 23, 217–233
• [2] Kubrusly C. S., Range-kernel complementation (to appear)
• [3] Lindenstrauss J., Tzafriri L., On the complemented subspaces problem, Israel J. Math., 1971, 9, 263–269
• [4] Kalton N. J., The complemented subspace problem revisited, Studia Math., 2008, 188, 223–257
• [5] Bennett G., Dor L. E., Goodman V., Johnson W. B., Newman, C. M., On uncomplemented subspaces of Lp, 1 < p < 2, Israel J. Math., 1977, 26, 178–187
• [6] Plichko A. M., Yost D., Complemented and uncomplemented subspaces of Banach spaces, Extracta Math., 2000, 15, 335–371
• [7] Müller V., Spectral theory of linear operators – and spectral systems in Banach algebras, 2nd ed., Birkhäuser, Basel, 2007
• [8] Kubrusly C. S., Spectral theory of operators on Hilbert spaces, Birkhäuser-Springer, New York, 2012
• [9] Conway J. B., A course in functional analysis, 2nd ed., Springer, New York, 1990
• [10] Halmos P. R., A Hilbert space problem book, 2nd ed., Springer, New York, 1982
• [11] Duggal B. P., Kubrusly C. S., Perturbation of Banach space operators with a complemented range, Glasgow Math. J., 2017, 59, 659–671
• [12] Harte R., Invertibility and singularity for bounded linear operators, Marcel Dekker, New York, 1988
• [13] Megginson R., An introduction to Banach space theory, Springer, New York, 1998
• [14] Kubrusly C. S., The elements of operator theory, Birkhäuser-Springer, New York, 2011
• [15] Rosenthal H. P., On the subspaces of Lp(p > 2) spanned by sequences of independent random variables, Israel J. Math., 1970, 8, 273–303
• [16] Campbell S. L., Faulkner G. D., Operators on Banach spaces with complemented ranges, Acta Math. Acad. Sci. Hungar., 1980, 35, 123–128

Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).