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On Musielak-Orlicz spaces isometric to L2 or L∞.

Anna Kaminska (1997)

Collectanea Mathematica

It is proved that a Musielak-Orlicz space LΦ of real valued functions which is isometric to a Hilbert space coincides with L2 up to a weight, that is Φ(u,t) = c(t) u2. Moreover it is shown that any surjective isometry between LΦ and L∞ is a weighted composition operator and a criterion for LΦ to be isometric to L∞ is presented.

On ( n , m ) - A -normal and ( n , m ) - A -quasinormal semi-Hilbertian space operators

Samir Al Mohammady, Sid Ahmed Ould Beinane, Sid Ahmed Ould Ahmed Mahmoud (2022)

Mathematica Bohemica

The purpose of the paper is to introduce and study a new class of operators on semi-Hilbertian spaces, i.e. spaces generated by positive semi-definite sesquilinear forms. Let be a Hilbert space and let A be a positive bounded operator on . The semi-inner product h k A : = A h k , h , k , induces a semi-norm · A . This makes into a semi-Hilbertian space. An operator T A ( ) is said to be ( n , m ) - A -normal if [ T n , ( T A ) m ] : = T n ( T A ) m - ( T A ) m T n = 0 for some positive integers n and m .

On n -normed spaces.

Gunawan, Hendra, Mashadi, M. (2001)

International Journal of Mathematics and Mathematical Sciences

On nilpotent operators

Laura Burlando (2005)

Studia Mathematica

We give several necessary and sufficient conditions in order that a bounded linear operator on a Banach space be nilpotent. We also discuss three necessary conditions for nilpotency. Furthermore, we construct an infinite family (in one-to-one correspondence with the square-summable sequences ( ε ) n of strictly positive real numbers) of nonnilpotent quasinilpotent operators on an infinite-dimensional Hilbert space, all the iterates of each of which have closed range. Each of these operators (as well as...

On (n,k)-quasiparanormal operators

Jiangtao Yuan, Guoxing Ji (2012)

Studia Mathematica

Let T be a bounded linear operator on a complex Hilbert space . For positive integers n and k, an operator T is called (n,k)-quasiparanormal if | | T 1 + n ( T k x ) | | 1 / ( 1 + n ) | | T k x | | n / ( 1 + n ) | | T ( T k x ) | | for x ∈ . The class of (n,k)-quasiparanormal operators contains the classes of n-paranormal and k-quasiparanormal operators. We consider some properties of (n,k)-quasiparanormal operators: (1) inclusion relations and examples; (2) a matrix representation and SVEP (single valued extension property); (3) ascent and Bishop’s property (β); (4) quasinilpotent...

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