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Partial isometries and EP elements in Banach algebras. (English) Zbl 1232.46044

Summary: New characterizations of partial isometries and EP elements in Banach algebras are presented.

MSC:

46H05 General theory of topological algebras
47A05 General (adjoints, conjugates, products, inverses, domains, ranges, etc.)
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[1] V. Rako, “Moore-Penrose inverse in Banach algebras,” Proceedings of the Royal Irish Academy. Section A, vol. 88, no. 1, pp. 57-60, 1988. · Zbl 0631.46045
[2] V. Rako, “On the continuity of the Moore-Penrose inverse in Banach algebras,” Facta Universitatis. Series: Mathematics and Informatics, no. 6, pp. 133-138, 1991. · Zbl 0774.46026
[3] P. Robert, “On the group-inverse of a linear transformation,” Journal of Mathematical Analysis and Applications, vol. 22, pp. 658-669, 1968. · Zbl 0159.32101 · doi:10.1016/0022-247X(68)90204-7
[4] E. Boasso, “On the Moore-Penrose inverse, EP Banach space operators, and EP Banach algebra elements,” Journal of Mathematical Analysis and Applications, vol. 339, no. 2, pp. 1003-1014, 2008. · Zbl 1129.47001 · doi:10.1016/j.jmaa.2007.07.059
[5] I. Vidav, “Eine metrische Kennzeichnung der selbstadjungierten Operatoren,” Mathematische Zeitschrift, vol. 66, pp. 121-128, 1956. · Zbl 0071.11503 · doi:10.1007/BF01186601
[6] C. Schmoeger, “Generalized projections in Banach algebras,” Linear Algebra and Its Applications, vol. 430, no. 2-3, pp. 601-608, 2009. · Zbl 1165.46026 · doi:10.1016/j.laa.2008.07.020
[7] E. Boasso and V. Rako, “Characterizations of EP and normal Banach algebra elements,” Linear Algebra and Its Applications, vol. 435, pp. 342-353, 2011. · Zbl 1228.47003 · doi:10.1016/j.laa.2011.01.031
[8] O. M. Baksalary, G. P. H. Styan, and G. Trenkler, “On a matrix decomposition of Hartwig and Spindelböck,” Linear Algebra and Its Applications, vol. 430, no. 10, pp. 2798-2812, 2009. · Zbl 1180.15004 · doi:10.1016/j.laa.2009.01.015
[9] O. M. Baksalary and G. Trenkler, “Characterizations of EP, normal, and Hermitian matrices,” Linear and Multilinear Algebra, vol. 56, no. 3, pp. 299-304, 2008. · Zbl 1151.15023 · doi:10.1080/03081080600872616
[10] S. Cheng and Y. Tian, “Two sets of new characterizations for normal and EP matrices,” Linear Algebra and Its Applications, vol. 375, pp. 181-195, 2003. · Zbl 1054.15022 · doi:10.1016/S0024-3795(03)00650-5
[11] D. S. Djordjević, “Products of EP operators on Hilbert spaces,” Proceedings of the American Mathematical Society, vol. 129, no. 6, pp. 1727-1731, 2001. · Zbl 0979.47002 · doi:10.1090/S0002-9939-00-05701-4
[12] D. S. Djordjević, “Characterizations of normal, hyponormal and EP operators,” Journal of Mathematical Analysis and Applications, vol. 329, no. 2, pp. 1181-1190, 2007. · Zbl 1155.47303 · doi:10.1016/j.jmaa.2006.07.008
[13] D. S. Djordjević and J. J. Koliha, “Characterizing Hermitian, normal and EP operators,” Filomat, vol. 21, no. 1, pp. 39-54, 2007. · Zbl 1273.47039 · doi:10.2298/FIL0701039D
[14] D. S. Djordjević, J. J. Koliha, and I. Stra\vskraba, “Factorization of EP elements in C\ast -algebras,” Linear and Multilinear Algebra, vol. 57, no. 6, pp. 587-594, 2009. · Zbl 1181.46041 · doi:10.1080/03081080802264372
[15] D. Drivaliaris, S. Karanasios, and D. Pappas, “Factorizations of EP operators,” Linear Algebra and Its Applications, vol. 429, no. 7, pp. 1555-1567, 2008. · Zbl 1155.47001 · doi:10.1016/j.laa.2008.04.026
[16] R. E. Hartwig and I. J. Katz, “On products of EP matrices,” Linear Algebra and Its Applications, vol. 252, pp. 339-345, 1997. · Zbl 0868.15015 · doi:10.1016/0024-3795(95)00693-1
[17] J. J. Koliha, “A simple proof of the product theorem for EP matrices,” Linear Algebra and Its Applications, vol. 294, no. 1-3, pp. 213-215, 1999. · Zbl 0938.15017 · doi:10.1016/S0024-3795(99)00066-X
[18] J. J. Koliha, “Elements of C\ast -algebras commuting with their Moore-Penrose inverse,” Studia Mathematica, vol. 139, no. 1, pp. 81-90, 2000. · Zbl 0963.46037
[19] G. Le\vsnjak, “Semigroups of EP linear transformations,” Linear Algebra and Its Applications, vol. 304, no. 1-3, pp. 109-118, 2000. · Zbl 0946.15009 · doi:10.1016/S0024-3795(99)00192-5
[20] D. Mosić, D. S. Djordjević, and J. J. Koliha, “EP elements in rings,” Linear Algebra and Its Applications, vol. 431, no. 5-7, pp. 527-535, 2009. · Zbl 1192.16039 · doi:10.1016/j.laa.2009.02.032
[21] D. Mosić and D. S. Djordjević, “Partial isometries and EP elements in rings with involution,” Electronic Journal of Linear Algebra, vol. 18, pp. 761-772, 2009. · Zbl 1192.16039
[22] D. Mosić and D. S. Djordjević, “EP elements in Banach algebras,” Banach Journal of Mathematical Analysis, vol. 5, no. 2, pp. 25-32, 2011. · Zbl 1232.46045
[23] P. Patrício and R. Puystjens, “Drazin-Moore-Penrose invertibility in rings,” Linear Algebra and Its Applications, vol. 389, pp. 159-173, 2004. · Zbl 1080.15004 · doi:10.1016/j.laa.2004.04.006
[24] A. Ben-Israel and T. N. E. Greville, Generalized Inverses: Theory and Applications, CMS Books in Mathematics/Ouvrages de Mathématiques de la SMC, 15, Springer, New York, NY, USA, 2nd edition, 2003. · Zbl 1026.15004
[25] S. L. Campbell and C. D. Meyer Jr., “EP operators and generalized inverses,” Canadian Mathematical Bulletin, vol. 18, no. 3, pp. 327-333, 1975. · Zbl 0317.15004 · doi:10.4153/CMB-1975-061-4
[26] J. J. Koliha, D. Djordjević, and D. Cvetković, “Moore-Penrose inverse in rings with involution,” Linear Algebra and Its Applications, vol. 426, no. 2-3, pp. 371-381, 2007. · Zbl 1130.46032 · doi:10.1016/j.laa.2007.05.012
[27] D. S. Djordjević and V. Rako, Lectures on Generalized Inverses, Faculty of Sciences and Mathematics, University of Ni\vs, Ni\vs, Serbia, 2008. · Zbl 1419.47001
[28] R. Harte and M. Mbekhta, “On generalized inverses in C\ast -algebras,” Studia Mathematica, vol. 103, no. 1, pp. 71-77, 1992. · Zbl 0810.46062
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