scholarly journals The properties of [∞,C]-isometric operators

Filomat ◽  
2019 ◽  
Vol 33 (14) ◽  
pp. 4541-4548
Author(s):  
Junli Shen ◽  
Kun Yu ◽  
Alatancang Chen
Keyword(s):  
Isometric Operator ◽  
Nilpotent Operator

In this paper we introduce the class of [?,C]-isometric operators and study various properties of this class. In particular, we show that if T is an [?,C]-isometric operator and Q is a quasi-nilpotent operator, then T + Q is an [?,C]-isometric operator under suitable conditions. Also, we show that the class of [?,C]-isometric operators is norm closed. Finally, we examine properties of products of [?,C]-isometric operators.

scholarly journals On [m,C]-isometric operators

Filomat ◽  
2017 ◽  
Vol 31 (7) ◽  
pp. 2073-2080 ◽  
Author(s):  
Muneo Chō ◽  
Ji Lee ◽  
Haruna Motoyoshi
Keyword(s):  
Hilbert Space ◽  
Tensor Product ◽  
Spectral Properties ◽  
Short Proof ◽  
Complex Hilbert Space ◽  
Isometric Operator ◽  
Nilpotent Operator

In this paper we introduce an [m;C]-isometric operator T on a complex Hilbert space H and study its spectral properties. We show that if T is an [m,C]-isometric operator and N is an n-nilpotent operator, respectively, then T + N is an [m + 2n ? 2,C]-isometric operator. Finally we give a short proof of Duggal?s result for tensor product of m-isometries and give a similar result for [m,C]-isometric operators.

scholarly journals A quasi-nilpotent operator with reflexive commutant, II

1999 ◽  
Vol 132 (2) ◽  
pp. 173-177 ◽  
Author(s):  
V. Müller ◽  
M. Zając
Keyword(s):  
Nilpotent Operator

scholarly journals NONRELATIVISTIC SPIN-½ PARTICLE IN AN ARBITRARY NON-ABELIAN MAGNETIC FIELD IN TWO SPATIAL DIMENSIONS

2002 ◽  
Vol 17 (02) ◽  
pp. 95-101
Author(s):  
T. E. CLARK ◽  
S. T. LOVE ◽  
S. R. NOWLING
Keyword(s):  
Magnetic Field ◽  
Positive Energy ◽  
Quantum Mechanical System ◽  
Zero Energy ◽  
Supersymmetry Algebra ◽  
Nilpotent Operator ◽  
Spin Particle ◽  
Spatial Dimensions ◽  
Hermitian Conjugate ◽  
Space Matrix

The (group and spin space) matrix Hamiltonian describing the dynamics of a non-relativistic spin-½ particle moving in a static, but spatially dependent, non-Abelian magnetic field in two spatial dimensions is shown to take the form of an anticommutator of a nilpotent operator and its Hermitian conjugate. Consequently, the (group space) matrix Hamiltonians for the two different spin projections form partners of a supersymmetric quantum mechanical system. The resulting supersymmetry algebra is exploited to explicitly construct the exact zero energy ground state wave function(s) for the system. The remaining eigenstates and eigenvalues of the two partner Hamiltonians form positive energy degenerate pairs.

scholarly journals Perturbation ofm-Isometries by Nilpotent Operators

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Teresa Bermúdez ◽  
Antonio Martinón ◽  
Vladimir Müller ◽  
Juan Agustín Noda
Keyword(s):  
Hilbert Space ◽  
Banach Spaces ◽  
Nilpotent Operator ◽  
Nilpotent Operators

We prove that ifTis anm-isometry on a Hilbert space andQann-nilpotent operator commuting withT, thenT+Qis a2n+m-2-isometry. Moreover, we show that a similar result form, q-isometries on Banach spaces is not true.

scholarly journals The general nilpotent operator system

2015 ◽  
Vol 261 ◽  
pp. 1-19 ◽  
Author(s):  
J. Dombi ◽  
O. Csiszár
Keyword(s):  
Nilpotent Operator ◽  
Operator System

On n-quasi-m-isometric operators

2016 ◽  
Vol 09 (04) ◽  
pp. 1650073 ◽  
Author(s):  
Salah Mecheri ◽  
T. Prasad
Keyword(s):  
Hilbert Space ◽  
Matrix Representation ◽  
Isometric Operator ◽  
Basic Properties

We introduce the class of [Formula: see text]-quasi-[Formula: see text]-isometric operators on Hilbert space. This generalizes the class of [Formula: see text]-isometric operators on Hilbert space introduced by Agler and Stankus. An operator [Formula: see text] is said to be [Formula: see text]-quasi-[Formula: see text]-isometric if [Formula: see text] In this paper [Formula: see text] matrix representation of a [Formula: see text]-quasi-[Formula: see text]-isometric operator is given. Using this representation we establish some basic properties of this class of operators.

scholarly journals On commutativity of C*-algebras

1987 ◽  
Vol 29 (1) ◽  
pp. 93-97 ◽  
Author(s):  
C.-S. Lin
Keyword(s):  
Hilbert Space ◽  
The Other ◽  
Nilpotent Operator ◽  
C Algebra ◽  
C Algebras ◽  
Adjoint Operators ◽  
Numerical Index

Two numerical characterizations of commutativity for C*-algebra (acting on the Hilbert space H) were given in [1]; one used the norms of self-adjoint operators in (Theorem 2), and the other the numerical index of (Theorem 3). In both cases the proofs were based on the result of Kaplansky which states that if the only nilpotent operator in is 0, then is commutative ([2] 2.12.21, p. 68). Of course the converse also holds.

scholarly journals (m, p)-isometric and (m, ∞)-isometric operator tuples on normed spaces

2015 ◽  
Vol 08 (02) ◽  
pp. 1550022 ◽  
Author(s):  
Philipp H. W. Hoffmann ◽  
Michael Mackey
Keyword(s):  
Hilbert Spaces ◽  
Normed Spaces ◽  
Isometric Operator ◽  
Natural Way

We generalize the notion of m-isometric operator tuples on Hilbert spaces in a natural way to operator tuples on normed spaces. This is done by defining a tuple analogue of (m, p)-isometric operators, so-called (m, p)-isometric operator tuples. We then extend this definition further by introducing (m, ∞)-isometric operator tuples and study properties of and relations between these objects.

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