On Certain Spaces of Ideal Operators

Wanjala Patrick Makila; Michael Onyango Ojiema; Achiles Nyongesa Simiyu

doi:10.51867/scimundi.3.1.9

Authors

Wanjala Patrick Makila
makilapatrick@yahoo.com
Department of Mathematics, Masinde Muliro University of Science and Technology, P.O.Box 190-50100, Kakamega, Kenya https://orcid.org/0009-0009-7454-2922
Michael Onyango Ojiema Department of Mathematics, Masinde Muliro University of Science and Technology, P.O.Box 190-50100, Kakamega, Kenya https://orcid.org/0000-0001-9635-7597
Achiles Nyongesa Simiyu Department of Mathematics, Masinde Muliro University of Science and Technology, P.O.Box 190-50100, Kakamega, Kenya https://orcid.org/0000-0001-5737-030X

Keywords:

Operator Ideals, Spaces of Ideal

Abstract

We determine some important spaces of ideal operators and ideal characteristics. Special consideration
is given to Frechet spaces, Spaces of finite rank operators and spaces of Hahn-Banach extension operators.
The characteristics of ideals and related properties in these spaces as well as in some of their dual spaces
are obtained.

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REFERENCES

Abrahamsen, T. A., Lima, A., and Lima, V. (2008). Unconditional ideals of finite rank operators. Czechoslovak Mathematical Journal, 58(4), 1257-1278. DOI: https://doi.org/10.1007/s10587-008-0085-9

Abrahamsen, T. A., and Nygaard, O. (2011). On λ-strict ideals in Banach spaces. Bulletin of the Australian Mathematical Society, 83(2), 231-240. DOI: https://doi.org/10.1017/S0004972710001735

Ayinde, S. A. (2022). Approximate Identities in Algebras of Compact Operators on Frechet Spaces, International Journal of Mathematical Sciences and Optimization: Theory and Applications Vol. 7, No. 2, pp. 133 - 143 DOI: https://doi.org/10.52968/28305203

Bence H. Algebras of operators on Banach spaces, and homomorphisms thereof. PhD Thesis, Lancaster University, 2019.

Godefroy, G., Kalton, N, J.and Saphar, P.D. (1988). “Duality in spaces of operators and smooth norms on Banach spaces”. Illinois J. Math.m, 32, 672-695. DOI: https://doi.org/10.1215/ijm/1255988868

Godefroy, G., Kalton, N, J.and Saphar, P.D. (1993). “Unconditional ideals in Banach spaces”. Studia mathematica, DOI: https://doi.org/10.4064/sm-104-1-13-59

(104), 13-59.

Harmad, P. and Lima A. (1984).“Banach spaces which are M-ideals in their biduals.”, Transactions of the American Mathematical Society, 283(1), 253-264. DOI: https://doi.org/10.1090/S0002-9947-1984-0735420-4

Harmad, P., Werner D., and Werner W. (1993).“M-ideals in Banach spaces and Banach algebras.”, springer-Verlag. DOI: https://doi.org/10.1007/BFb0084355

Lima.V, Lima.A and Nygaard.O., (2004). “On the compact approximation property”, Studia math., 160, 185-200. DOI: https://doi.org/10.4064/sm160-2-6

Lima Asvald, (1979). “M-Ideals of compact operators in classical Banach spaces”, Math.Scand., 44, 207-217. DOI: https://doi.org/10.7146/math.scand.a-11804

Lima Asvald, (1993). “The metric approximation, norm-one projections and intersection properties of balls”. Israel J. Math., 84, 451-475. DOI: https://doi.org/10.1007/BF02760953

Lima. V,Lima.A. , (2009). “Strict u-ideals in Banach spaces”, Studia Math., 3(195), 275-285. DOI: https://doi.org/10.4064/sm195-3-6

Lima, A and Oja, E.Rao,T.S.S.R.K. and Werner D., (1973). Geometry of operator spaces, Michigan Math.J., 41, 473-490. DOI: https://doi.org/10.1307/mmj/1029005074

Linus C. Ideals and Boundaries in Algebras of Holomorphic Functions. Umea University, Doctoral Thesis, No. 33, 2006.

Mallios A. , Topological Algebras—Selected Topics, North-Holland Math. Stud., vol. 124, 1986.

Mathews D. Banach algebras of operators. PhD Thesis. University of Leeds, 2004.

Martsinkevits, J., and Poldvere, M. (2019). On the structure of the dual unit ball of strict u-ideals. DOI: https://doi.org/10.1215/20088752-2018-0007

Maurya, R. (2022). A study of some classes of operators on Banach spaces (Doctoral dissertation, Indian Institute of Information Technology Allahabad).

Patel S. R. (2011). Closed ideals of A∞ and a famous problem of Grothendieck. Rev. Mat. Iberoamericana 27 (2011), no. 3, 977–995 DOI: https://doi.org/10.4171/RMI/660

Saeid J. and Seith P. M. (2020). On Properties of slightly λ− Continuous functions. Preprint

Sonia S. On One-sided M-structure of operator spaces and operator Algebras. PhD Theis, the University of Houston, 2009.