SOME EQUIVALENT QUASINORMS ON L_fi;E

Pınar Zengin Alp, Emrah Evren Kara

DOI Number
-
First page
739
Last page
749

Abstract


In this paper we define a new opertaor ideal L_fi;E by using block sequence spaces and symmetric norming function. Also we define different quasi-norms on this class and deal with equivalence of these quasi-norms.

Keywords

Operator ideal; sequence spaces; norming function; quasi-norm

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References


A. Pietsch, Einigie neu Klassen von Kompakten linearen Abbildungen, revue Roum. Math.

Pures et Appl., 8, 427-447, 1963.

A. Ma ji, P.D. Srivastava, On operator ideals using weighted Ces‡ro sequence space, Egyptian

Math.Soc., 22(3), 446-452, 2014.

I. J. Maddox, Spaces of strongly summable sequences, Quart. J. Math. Oxford, 18(2), 345-355,

B. Altay, F. Ba¸sar, Generalization of the sequence space l (p) derived by weighted mean, J.

Math. Anal. Appl, 330, 174-185, 2007.

E. Malkowsky and E. Sava¸s, Matrix transformations between sequence spaces of generalized

weighted means, Appl. Math. Comp. 147, 333-345, 2004.

J. S. Shiue, On the Cesaro sequence spaces, Tamkang J. Math. 1(1), 19ñ25, 1970.

S. Saejung, Another look at Cesaro sequence spaces, J. Math.Anal. Appl. 366 (2), 530ñ537,

N. ¸Sim¸sek,V. Karakaya, H. Polat, Operators ideals of generalized modular spaces of Cesaro

type deÖned by weighted means, J. Comput. Anal. Appl. 19(1), 804-811, 2015.

B.Carl, A.Hinrichs, On s-numbers and Weyl inequalities of operators in Banach spaces,

Bull.Lond. Math. Soc., 41(2), 332-340, 2009.

Gh. Constantin, Operators of ces

p type, Rend. Acc. Naz.Lincei., 52 (8), 875ñ878, 1972.

B.E. Rhoades, Operators of A-p type, Atti Accad. Naz. Lincei.Rend. Cl. Sci. Fis. Mat. Natur.

(8), 1975, no. 3ñ4, 238ñ241, 1976.

N. Tita, On Stolz mappings, Math. Japonica 26 (4), 495ñ496, 1981.

A. Ma ji, P.D. Srivastava, Some class of operator ideals, Int. J. Pure Appl. Math., 83 (5),

-740, 2013.

A. Ma ji, P.D. Srivastava, Some results of operator ideals on stype

jA; pj operators, Tamkang

J. Math., 45 (2), 119-136, 2014.

E. E. Kara, M. Ilkhan, On a new class of s-type operators, Konuralp J. Math., 3(1), 1-11, ·

A. Pietsch, Operator Ideals, VEB Deutscher Verlag der Wissenschaften, Berlin, 1978.

N.Tita, Some equivalent quasinorms on operator ideals, Spectral and Evolution Problems,

Taurida National Univ. Simferopol, 13, 103-108, 2002.

N. Tita, Cuasinorme echivalente pe spatii de aproximare, Ed. Univ. Tranilvania, Brasov,

N. Salinas, Symmetric norm ideals and relative conjugate ideals,Trans. A.M.S., 188, 213-240,

N. Tita, Generalized s-numbers operator ideals, The Annual Conference of the Romanian

Society of Mathematical Sciences, May 29-June 1, Bucharest, Romania, 1997.

I. Gohberg, M.Krein, Introduction to the theory of non-selfadjoint operators, A.M.S. Providence,

N. Tita, Operatori de clasa p;; Studii cercet. Mat.23, 467-487, 1971.

N.Tita: On a class of `; operators, Collect. Mat. 32, 275-279, 1981.

R. Schatten, Norm ideals of completely continuous operators, Springer Verlag, 1960.

P. Zengin Alp, M. Ilkhan, E. E. Kara, Generalized Stolz mappings, Konuralp J. Math., 5 (2), ·

-18, 2017.

P. Zengin Alp, E. E. Kara, A new class of operator ideals and approximation numbers, New

Trend Math. Sci. , In pr

EQU IVALENT QUASINORM S 9

N. Tita, Ideale de operatori generate de s numere, Ed. Univ. Tranilvania, Brasov, 1998.

D. Foroutannia, On the block sequence space lp (E) and related matrix transformations,

TurkJ. Math., (39), 830-841, 2015.

H Roopaei, D Foroutannia, The norm of certain matrix operators on new di§erence sequence

spaces, Jordan J. Math.Stat. 8 (3), 223 - 237, 2015.

H Roopaei, D Foroutannia, A new sequence space and norm of certain matrix operators on

this space, Sahand Communications in Mathematical Analysis (SCMA), 3 (1), 1-12, 2016.

P. Zengin Alp, E. E. Kara, A new class of operator ideals on the block sequence space lp (E) ;

Submitted, 2018

M. Mursaleen, V. A. Khan, Generalized Cesaro vector-valued sequence space and matrix

transformations, Information Sciences, 173, 11-21, 2005.


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