Antinormal Composition Operators on the L2-Space of an Atomic Measure Space

2019 ◽  
Vol 71 (1) ◽  
pp. 102-110
Author(s):  
D. Kumar ◽  
H. Chandra
Keyword(s):  
Measure Space ◽  
Composition Operators ◽  
Atomic Measure

scholarly journals Composition operators in Orlicz spaces

2004 ◽  
Vol 76 (2) ◽  
pp. 189-206 ◽  
Author(s):  
Yunan Cui ◽  
Henryk Hudzik ◽  
Romesh Kumar ◽  
Lech Maligranda
Keyword(s):  
Composition Operator ◽  
Measure Space ◽  
Composition Operators ◽  
Orlicz Spaces

AbstractComposition operators Cτ between Orlicz spaces Lϕ (Ω, Σ, μ) generated by measurable and nonsingular transformations τ from Ω into itself are considered. We characterize boundedness and compactness of the composition operator between Orlicz spaces in terms of properties of the mapping τ, the function ϕ and the measure space (Ω, Σ, μ). These results generalize earlier results known for Lp-spaces.

scholarly journals M-Cohyponormal powers of composition operators

1992 ◽  
Vol 53 (1) ◽  
pp. 9-16
Author(s):  
Satish K. Khurana ◽  
Babu Ram
Keyword(s):  
Composition Operator ◽  
Measure Space ◽  
Composition Operators ◽  
Finite Measure ◽  
Finite Measure Space ◽  
Positive Integers ◽  
Nikodym Derivative

AbstractLet T1, i = 1, 2 be measurable transformations which define bounded composition operators C Ti on L2 of a σ-finite measure space. Let us denote the Radon-Nikodym derivative of with respect to m by hi, i = 1, 2. The main result of this paper is that if and are both M-hyponormal with h1 ≤ M2(h2 o T2) a.e. and h2 ≤ M2(h1 o T1) a.e., then for all positive integers m, n and p, []* is -hyponormal. As a consequence, we see that if is an M-hyponormal composition operator, then is -hyponormal for all positive integers n.

scholarly journals Weighted composition operators on functional Hilbert spaces

1985 ◽  
Vol 31 (1) ◽  
pp. 117-126 ◽  
Author(s):  
R.K. Singh ◽  
R. David Chandra Kumar
Keyword(s):  
Hilbert Spaces ◽  
Composition Operators ◽  
Weighted Composition Operator ◽  
Linear Operators ◽  
Weighted Composition Operators ◽  
Bounded Linear ◽  
Atomic Measure ◽  
Weighted Composition ◽  
Functional Hilbert Spaces

Let X be a non-empty set and let H(X) denote a Hibert space of complex-valued functions on X. Let T be a mapping from X to X and θ a mapping from X to C such that for all f in H(X), f ° T is in H(x) and the mappings CT taking f to f ° T and M taking f to θ.f are bounded linear operators on H(X). Then the operator CTMθ is called a weighted composition operator on H(X). This note is a report on the characterization of weighted composition operators on functional Hilbert spaces and the computation of the adjoint of such operators on L2 of an atomic measure space. Also the Fredholm criteria are discussed for such classes of operators.

scholarly journals Introducing Atomic Separation Axioms on Atomic Measure Space – An Advanced Study

2014 ◽  
Vol 10 (5) ◽  
pp. 18-29
Author(s):  
S. C. P Halakatti ◽  
◽  
Akshata Kengangutti
Keyword(s):  
Measure Space ◽  
Separation Axioms ◽  
Advanced Study ◽  
Atomic Measure

COMPACT WEIGHTED COMPOSITION OPERATORS BETWEEN -SPACES

2020 ◽  
Vol 102 (1) ◽  
pp. 151-161 ◽  
Author(s):  
CHING-ON LO ◽  
ANTHONY WAI-KEUNG LOH
Keyword(s):  
Measure Space ◽  
Composition Operators ◽  
Weighted Composition Operators ◽  
Weighted Composition

We provide complete characterisations for the compactness of weighted composition operators between two distinct $L^{p}$-spaces, where $1\leq p\leq \infty$. As a corollary, when the underlying measure space is nonatomic, the only compact weighted composition map between $L^{p}$-spaces is the zero operator.

WEIGHTED COMPOSITION OPERATORS BETWEEN LORENTZ SPACES

2020 ◽  
pp. 1-13
Author(s):  
CHING-ON LO ◽  
ANTHONY WAI-KEUNG LOH
Keyword(s):  
Measure Space ◽  
Composition Operators ◽  
Lorentz Spaces ◽  
Weighted Composition Operators ◽  
Weighted Composition

Abstract We investigate the boundedness, compactness, invertibility and Fredholmness of weighted composition operators between Lorentz spaces. It is also shown that the classes of Fredholm and invertible weighted composition maps between Lorentz spaces coincide when the underlying measure space is nonatomic.

scholarly journals Local monotonicity coefficients in Orlicz sequence spaces equipped with the p-Amemiya norm

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Xin He ◽  
Yunan Cui ◽  
Henryk Hudzik
Keyword(s):  
Measure Space ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Orlicz Sequence Space ◽  
Atomic Measure ◽  
Uniform Monotonicity ◽  
Orlicz Sequence Spaces ◽  
Necessary And Sufficient ◽  
Local Monotonicity ◽  
Amemiya Norm

Abstract In this paper, the monotonicity is investigated with respect to Orlicz sequence space $l_{\varPhi , p}$ l Φ , p equipped with the p-Amemiya norm, and the necessary and sufficient condition is obtained to guarantee the uniform monotonicity, locally uniform monotonicity, and strict monotonicity for $l_{\varPhi , p}$ l Φ , p . This completes the results of the paper (Cui et al. in J. Math. Anal. Appl. 432:1095–1105, 2015) which were obtained for the non-atomic measure space. Local upper and lower coefficients of monotonicity at any point of the unit sphere are calculated, $l_{\varPhi , p}$ l Φ , p is calculated.

An inner measure associated with a von Neumann algebra

1968 ◽  
Vol 64 (3) ◽  
pp. 645-650 ◽  
Author(s):  
G. de Barra
Keyword(s):  
Hilbert Space ◽  
Finite Type ◽  
Measure Space ◽  
Von Neumann Algebra ◽  
Dimension Function ◽  
Type Ii ◽  
Von Neumann ◽  
Linear Sets ◽  
Atomic Measure ◽  
Starting Point

An ‘inner measure’ analogous to Lebesgue inner measure and associated with a von Neumann algebra is constructed on the linear sets of a Hilbert space. We supposed to be of finite type and countably decomposable, as these restrictions will be necessary for some of the results obtained. As remarked by Dye in (2), Type II1 algebras have a structure analogous to that of a finite non-atomic measure space, the trace corresponding to the measure. We define a class of ‘measurable sets’ and obtain some of its properties. The development of the theory is indicated also from the starting point of a function-valued dimension function. The idea for the construction of such an inner measure comes from a remark in (3), paragraph 16·2, and the terminology of (3) and of (5) is used throughout.

scholarly journals Subnormal Weighted Shifts on Directed Trees and Composition Operators inL2-Spaces with Nondensely Defined Powers

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Piotr Budzyński ◽  
Piotr Dymek ◽  
Zenon Jan Jabłoński ◽  
Jan Stochel
Keyword(s):  
Positive Integer ◽  
Composition Operator ◽  
Measure Space ◽  
Composition Operators ◽  
Finite Measure ◽  
Weighted Shift ◽  
Weighted Shifts ◽  
Directed Tree ◽  
Finite Measure Space ◽  
Densely Defined

It is shown that for every positive integernthere exists a subnormal weighted shift on a directed tree (with or without root) whosenth power is densely defined while its (n+1)th power is not. As a consequence, for every positive integernthere exists a nonsymmetric subnormal composition operatorCin anL2-space over aσ-finite measure space such thatCnis densely defined andCn+1is not.

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