Mohamed Ech-chad | Yokohama National University (original) (raw)

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Papers by Mohamed Ech-chad

Revista Colombiana de Matemáticas

Let H be a separable infinite dimensional complex Hilbert space, and let L(H) denote the algebra ... more Let H be a separable infinite dimensional complex Hilbert space, and let L(H) denote the algebra of all bounded linear operators on H into itself. Given A, B ∈ L(H), define the generalized derivation δA, B ∈ L(L(H)) by δA, B(X) = AX - XB. An operator A ∈ L(H) is P-symmetric if AT = TA implies AT* = T* A for all T ∈ C1(H) (trace class operators). In this paper, we give a generalization of P-symmetric operators. We initiate the study of the pairs (A, B) of operators A, B ∈ L(H) such that R(δA, B) W* = R(δA, B) W*, where R(δA, B) W* denotes the ultraweak closure of the range of δA, B. Such pairs of operators are called generalized P-symmetric. We establish a characterization of those pairs of operators. Related properties of P-symmetric operators are also given.

Methods of Functional Analysis and Topology

... Examinateurs : M. BOUALI SAID, PES, ( FS, Kénitra ). M. ZEROUALI EL HASSAN, PES, ( FS, Rabat ... more ... Examinateurs : M. BOUALI SAID, PES, ( FS, Kénitra ). M. ZEROUALI EL HASSAN, PES, ( FS, Rabat ). M. BOUSSEJRA ABDELHAMID, PES, ( FS, Kénitra ). M. KHAOULANI BOUCHTA, PES, ( ENIM, Rabat ). M. INTISSAR AHMED, PES, ( FS, Rabat ). ...

TURKISH JOURNAL OF MATHEMATICS

In this paper we establish some properties concerning the class of operators A ∈ L(H) that satisf... more In this paper we establish some properties concerning the class of operators A ∈ L(H) that satisfy R(δA) ∩ {A} ′ = {0} , where R(δA) is the norm closure of the range of the inner derivation δA, defined on L(H) by δA(X) = AX −XA. Here H stands for a Hilbert space; as a consequence, we show that the set {A ∈ L(H) / R(δA)∩{A} ′ = {0}} is norm-dense. We also describe some classes of operators A, B for which we have R(δA,B) ∩ ker(δA * ,B *) = {0} (ker(δA * ,B *) is the kernel of the generalized derivation δA * ,B * defined on L(H) by δA * ,B * (X) = A * X − XB *).

Let T be a w-hyponormal operator with the polar decomposition T U[ 7]. In this paper, we show the... more Let T be a w-hyponormal operator with the polar decomposition T U[ 7]. In this paper, we show the following:

Revista Colombiana de Matemáticas

Let H be a separable infinite dimensional complex Hilbert space, and let L(H) denote the algebra ... more Let H be a separable infinite dimensional complex Hilbert space, and let L(H) denote the algebra of all bounded linear operators on H into itself. Given A, B ∈ L(H), define the generalized derivation δA, B ∈ L(L(H)) by δA, B(X) = AX - XB. An operator A ∈ L(H) is P-symmetric if AT = TA implies AT* = T* A for all T ∈ C1(H) (trace class operators). In this paper, we give a generalization of P-symmetric operators. We initiate the study of the pairs (A, B) of operators A, B ∈ L(H) such that R(δA, B) W* = R(δA, B) W*, where R(δA, B) W* denotes the ultraweak closure of the range of δA, B. Such pairs of operators are called generalized P-symmetric. We establish a characterization of those pairs of operators. Related properties of P-symmetric operators are also given.

Methods of Functional Analysis and Topology

... Examinateurs : M. BOUALI SAID, PES, ( FS, Kénitra ). M. ZEROUALI EL HASSAN, PES, ( FS, Rabat ... more ... Examinateurs : M. BOUALI SAID, PES, ( FS, Kénitra ). M. ZEROUALI EL HASSAN, PES, ( FS, Rabat ). M. BOUSSEJRA ABDELHAMID, PES, ( FS, Kénitra ). M. KHAOULANI BOUCHTA, PES, ( ENIM, Rabat ). M. INTISSAR AHMED, PES, ( FS, Rabat ). ...

TURKISH JOURNAL OF MATHEMATICS

In this paper we establish some properties concerning the class of operators A ∈ L(H) that satisf... more In this paper we establish some properties concerning the class of operators A ∈ L(H) that satisfy R(δA) ∩ {A} ′ = {0} , where R(δA) is the norm closure of the range of the inner derivation δA, defined on L(H) by δA(X) = AX −XA. Here H stands for a Hilbert space; as a consequence, we show that the set {A ∈ L(H) / R(δA)∩{A} ′ = {0}} is norm-dense. We also describe some classes of operators A, B for which we have R(δA,B) ∩ ker(δA * ,B *) = {0} (ker(δA * ,B *) is the kernel of the generalized derivation δA * ,B * defined on L(H) by δA * ,B * (X) = A * X − XB *).

Let T be a w-hyponormal operator with the polar decomposition T U[ 7]. In this paper, we show the... more Let T be a w-hyponormal operator with the polar decomposition T U[ 7]. In this paper, we show the following: