Hypo-q-norms on a cartesian product of algebras of operators on Banach spaces

Silvestru Sever Dragomir

Published: 2020-02-01

Vol. 34 No. 2 (2020)

Hypo-q-norms on a cartesian product of algebras of operators on Banach spaces

Silvestru Sever Dragomir

Abstract

In this paper we consider the hypo-q-operator norm and hypo-q-numerical radius on a Cartesian product of algebras of bounded linear operators on Banach spaces. A representation of these norms in terms of semi-inner products, the equivalence with the q-norms on a Cartesian product and some reverse inequalities obtained via the scalar reverses of Cauchy-Buniakowski-
Schwarz inequality are also given.

Keywords:

normed spaces , cartesian products of normed spaces , inequalities , reverse inequalities , Shisha-Mond type inequalities

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Dragomir, S. S. (2020). Hypo-q-norms on a cartesian product of algebras of operators on Banach spaces. Annales Mathematicae Silesianae, 34(2), 169–192. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/13610

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References

1. S.S. Dragomir, A survey on Cauchy-Bunyakovsky-Schwarz type discrete inequalities, J. Inequal. Pure Appl. Math. 4 (2003), no. 3, Art. 63, 142 pp. Available at https://www.emis.de/journals/JIPAM/article301.html?sid=301.
2. S.S. Dragomir, A counterpart of Schwarz’s inequality in inner product spaces, East Asian Math. J. 20 (2004), no. 1, 1–10. Preprint RGMIA Res. Rep. Coll. 6 (2003), Supplement, Art. 18. Available at http://rgmia.org/papers/v6e/CSIIPS.pdf.
3. S.S. Dragomir, Semi-Inner Products and Applications, Nova Science Publishers, Inc., Hauppauge, NY, 2004.
4. S.S. Dragomir, Advances in Inequalities of the Schwarz, Grüss and Bessel Type in Inner Product Spaces, Nova Science Publishers, Inc., Hauppauge, NY, 2005.
5. S.S. Dragomir, Reverses of the Schwarz inequality generalising a Klamkin-McLenaghan result, Bull. Austral. Math. Soc. 73 (2006), no. 1, 69–78.
6. S.S. Dragomir, The hypo-Euclidean norm of an n-tuple of vectors in inner product spaces and applications, J. Inequal. Pure Appl. Math. 8 (2007), no. 2, Art. 52, 22 pp. Available at https://www.emis.de/journals/JIPAM/article854.html?sid=854.
7. S.S. Dragomir, Hypo-q-norms on a Cartesian product of normed linear spaces, Preprint RGMIA Res. Rep. Coll. 20 (2017), Art. 153. Available at http://rgmia.org/papers/v20/v20a153.pdf.
8. S.S. Dragomir, Inequalities for hypo-q-norms on a Cartesian product of inner product spaces, Preprint RGMIA Res. Rep. Coll. 20 (2017), Art. 168. Available at http://rgmia.org/papers/v20/v20a168.pdf.
9. J.R. Giles, Classes of semi-inner-product spaces, Trans. Amer. Math. Soc. 129 (1967), 436–446.
10. B.W. Glickfeld, On an inequality of Banach algebra geometry and semi-inner product space theory, Illinois J. Math. 14 (1970), 76–81.
11. G. Lumer, Semi-inner-product spaces, Trans. Amer. Math. Soc. 100 (1961), 29–43.
12. P.M. Miličić, Sur le semi-produit scalaire dans quelques espaces vectoriels normés, Mat. Vesnik 8(23) (1971), 181–185.
13. P.M. Miličić, Une généralisation naturelle du produit scalaire dans un espace normé et son utilisation, Publ. Inst. Math. (Beograd) (N.S.) 42(56) (1987), 63–70.
14. P.M. Miličić, La fonctionelle g et quelques problèmes des meilleures approximations dans des espaces normés, Publ. Inst. Math. (Beograd) (N.S.) 48(62) (1990), 110–118.
15. M.S. Moslehian, M. Sattari and K. Shebrawi, Extensions of Euclidean operator radius inequalities, Math. Scand. 120 (2017), no. 1, 129–144.
16. B. Nath, On a generalization of semi-inner product spaces, Math. J. Okayama Univ. 15 (1971), no. 1, 1–6.
17. P.L. Papini, Un’osservazione sui prodotti semi-scalari negli spazi di Banach, Boll. Un. Mat. Ital. (4) 2 (1969), 686–689.
18. I. Roşca, Semi-produit scalaire et représentations de type de Riesz pour les fonctionelles linéaires et bornées sur les espaces normés, C.R. Acad. Sci. Paris Sér. A-B 283 (1976), no. 3, Ai, A79–A81.
19. O. Shisha and B. Mond, Bounds on differences of means, in: O. Shisha (ed.), Inequalities, Academic Press, Inc., New York, 1967, pp. 293–308. Google Scholar

Vol. 34 No. 2 (2020)
Published: 2020-09-01

ISSN: 0860-2107

eISSN: 2391-4238

10.2478/amsil

Publisher

University of Silesia Press

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