Range-Kernel orthogonality and elementary operators on certain Banach spaces

• Autorzy: Bachir Ahmed , Segres Abdelkader , Sayyaf Nawal Ali , Ouarghi Khalid

Identyfikatory

DOI

10.1515/dema-2021-0024

• Języki publikacji: EN

Abstrakty

EN

The characterization of the points in Cp:1≤p<∞(H) , the Von Neuman-Schatten p-classes, that are orthogonal to the range of elementary operators has been done for certain kinds of elementary operators. In this paper, we shall study this problem of characterization on an abstract reflexive, smooth and strictly convex Banach space for arbitrary operator. As an application, we consider other kinds of elementary operators defined on the spaces Cp:1≤p<∞(H), and finally, we give a counterexample to Mecheri’s result given in this context.

Słowa kluczowe

EN

Range-Kernel orthogonality; elementary operators; Schatten p-classes; trace class operators

PL

ortogonalność; operatory elementarne; klasy Schattena; operatory śladowe

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2021
• Tom: Vol. 54, nr 1
• Strony: 272--279
• Opis fizyczny: Bibliogr. 14 poz.

Twórcy

autor

Bachir Ahmed

• Department of Mathematics, King Khalid University, Abha, Saudi Arabia

autor

Segres Abdelkader

• Department of Mathematics, University of Mascara, Mascara, Algeria

autor

Sayyaf Nawal Ali

• Department of Mathematics, University of Bisha, Bisha, Saudi Arabia

autor

Ouarghi Khalid

• Department of Mathematics, King Khalid University, Abha, Saudi Arabia

Bibliografia

• [1] R. Bhatia and F. Kittaneh, Norm inequalities for partitioned operators and an application, Math. Ann. 287 (1990), 719–726.
• [2] A. Bachir and A. Segres, Generalized Fuglede-Putnam’s theorem and orthogonality, AJMAA 1 (2004), 1–5.
• [3] R. C. James, Orthogonality and linear functionals in normed linear spaces, Trans. Amer. Math. Soc. 61 (1947), 265–292.
• [4] R. Harte, Skew exactness and range-kernel orthogonality, Filomat 19 (2005), 19–33.
• [5] J. Anderson, On normal derivations, Proc. Amer. Math. Soc. 38 (1973), 136–140.
• [6] M. Amouch, A note on the range of generalized derivation, Extracta Math. 23 (2008), no. 3, 235–242.
• [7] M. Amouch, Range, kernel orthogonality and operator equations, Extracta Math. 21 (2008), no. 2, 149–157.
• [8] B. P. Duggal, Subspace gaps and range-kernel orthogonality of an elementary operator, Linear Algebra Appl. 383 (2004), 93–106.
• [9] B. P. Duggal, Range-kernel orthogonality of the elementary operator (…), Linear Algebra Appl. A 337 (2001), 79–86.
• [10] B. Simon, Trace ideals and their applications, London Mathematical Society Lecture Note Series, vol. 35, Cambridge University Press, Cambridge, 1979.
• [11] J. R. Holub, On the metric geometry of ideals of operators on Hilbert space, Math. Ann. 201 (1973), 157–163.
• [12] R. R. Phelps, Convex functions, monotone operators and differentiability, Lecture Notes in Mathematics, vol. 1364, Springer-Verlag, New York, 1993.
• [13] B. P. Duggal, Putnam-Fuglede theorem and the range-kernel orthogonality of derivations, Int. J. Math. Math. Sci. 27 (2001), 573–582.
• [14] S. Mecheri, Gâteaux derivative and orthogonality in Cp-classes, J. Inequal. Pure Appl. 7 (2006), no. 2, 77.

Uwagi

PL

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).