Essential Norm Research Articles

Essential norm of the differences of composition operators on the Bloch space

Essential norm of the differences of composition operators on the Bloch space

Essential Norms of Volterra Type Operators between Zygmund Type Spaces

We investigate the boundedness of some Volterra type operators between Zygmund type spaces. Then, we give the essential norms of such operators in terms of g,φ, their derivatives, and the nth power φn of φ.

Inequalities involving norm and essential norm of weighted composition operators

Inequalities involving norm and essential norm of weighted composition operators

AN ANALYSIS OF REGIME CAPACITY AND A NASCENT ENVIRONMENTAL CONFLICT IN THE NIGER RIVER BASIN

The Niger River Basin (RNB) is and has been important to the cultural and socio-economic development of the West African region. However, the basin, which is home to some of the poorest countries in the world, might be experiencing a new landscape of conflict with water resources being a key factor. A combination of climate change, human population growth and unsustainable resource use is threatening the RNB. The purpose of this article is to determine, through the Homer-Dixon Environmental Scarcity Theory, the impact and effects of environmental scarcity in contributing to a nascent conflict in the RNB. The article conceptualises Homer-Dixon’s Environmental Scarcity Theory as a theory that argues for the potential of conflict in transboundary river basins as a result of environmental scarcity. Furthermore, the article conceptualises Regime Theory, particularly in the RNB, as treaties on international rivers that hold essential norms and encourage rule-based cooperation to politically resolve problems and conflict in the field of international river basin management. The article will therefore use Regime Theory to examine the existence and formation, role and progress (i.e. successes and challenges) of the regimes and/or institutional mechanisms that aim to deal with environmental scarcity in the RNB.

Essential norm of generalized composition operators on Zygmund type spaces and Bloch type spaces

Essential norm of generalized composition operators on Zygmund type spaces and Bloch type spaces

Essential norm of substitution vector-valued integral operator on L1(Σ) space

In this paper, we determine essential norm of a substitution vector-valued integral operator Tuφ on L1(Σ) space using conditional expectation operators.

Composition Operators in Bloch Spaces of Slice Hyperholomorphic Functions

In this paper we define Bloch-type spaces of slice hyperholomorphic functions in the unit ball \(\mathbb {B}.\) We study the invariance of these spaces with slice regular Mobius transformation and also give some simple characterizations for boundedness and compactness of composition operators on the slice regular Bloch-type spaces on the unit ball \(\mathbb {B}.\) We also estimate the essential norm of these operators.

Weighted differentiation composition operators from the logarithmic Bloch space to the weighted-type space

Abstract The boundedness of the weighted differentiation composition opera- tor from the logarithmic Bloch space to the weighted-type space is characterized in terms of the sequence (zn)n∈N0. An asymptotic estimate of the essential norm of the operator is also given in terms of the sequence, which gives a characterization for the compactness of the operator.

Composition Operators on Weighted Banach Spaces of a Tree

We study composition operators on the weighted Banach spaces of an infinite tree. We characterize the bounded and the compact operators, as well as determine the operator norm and the essential norm. In addition, we study the isometric composition operators.

A New Characterization of Differences of Weighted Composition Operators on Weighted-Type Spaces

In this paper, we give a new characterization for the boundedness, compactness and essential norm of differences of weighted composition operators between weighted-type spaces.

Differences of Composition Operators on Bloch Type Spaces

In this paper, we study the boundedness, compactness and essential norm of differences of composition operators \(C_{\varphi }-C_{\psi }\) on Bloch type spaces. In particular, we use the Bloch type norm of \(\varphi ^n-\psi ^n\) to characterize these.

New essential norm estimates of weighted composition operators from H∞ into the Bloch space

In this paper, we give new essential norm estimates of weighted composition operators from into the Bloch space, where u is a function analytic on the unit disc and is an analytic self-map of . Moreover, a new characterization for the boundedness and compactness of the weighted composition operators is obtained by the nth power of the symbol and the Volterra operators and .

Topological Structure of the Spaces of Composition Operators on Hilbert Spaces of Dirichlet Series

In this paper we study some topological properties of the space of bounded composition operators on some Hilbert spaces of Dirichlet series. We first obtain formulas for the norms and essential norms of composition operators and differences of composition operators on Hilbert spaces of Dirichlet series. Then we give a characterization of the isolated points in the topological space of bounded composition operators on some Hilbert spaces of Dirichlet series. Finally we obtain sufficient conditions such that two composition operators are in the same path component. We show, among other results, that all compact composition operators are in the same path component. For a certain class of frequencies we give complete description of path components.

A note on the essential norm of weighted composition operators on BMOA

We give some new estimates for the essential norm of weighted composition operators on the space BMOA. As a corollary, we obtain a new characterization for the compactness of weighted composition operators on the space BMOA.

Essential norm of a Volterra-type integral operator from Hardy spaces to some analytic function spaces

In this paper, we obtain some estimates of essential norm of the Volterra-type integral operator $T_g$, where \[ T_gf(z)=\int ^z_0f(\zeta )g'(\zeta )\,d\zeta , \] from Hardy spaces to the BMOA space, Besov spaces, Berg\-man spaces and Bloch-type spaces.

Essential norm of weighted composition operators from H∞ to the Zygmund space

Essential norm of weighted composition operators from H∞ to the Zygmund space

Weighted differentiation composition operator from logarithmic Bloch spaces to Bloch‐type spaces

In this paper, we give a new characterization for the boundedness of weighted differentiation composition operator from logarithmic Bloch spaces to Bloch‐type spaces and calculate its essential norm in terms of the n‐th power of induced analytic self‐map on the unit disk. From which a sufficient and necessary condition of compactness of this operator follows immediately.

The Contract of Employment and the Paradoxes of Precarity

In recent decades, and with increasing acceleration in the last ten years, the law and practice of the contract of employment in the United Kingdom have been dissolving themselves from a state in which a stable contract of employment represented the essential norm into a complex of precarious types of employment relation. This descent into precarity presents us with several legal and practical paradoxes. Perhaps the deepest of these is the emergence into a centrally prominent position of the so-called ‘zero-hours contract’ - a paradoxical development in the sense that, in many of its forms, this kind of employment relation should not be regarded as an employment contract at all. Another one consists of the abolition of mandatory retirement age in the name of control of age discrimination; ostensibly increasing the security of employment of the older worker, this measure, it will be argued, in fact makes employment more precarious than ever, effectively undermining the notion of ‘permanent employment’. This paper examines the legal bases, but also the profound social and economic consequences, of these ironical developments.

Essential Norm of Weighted Composition Operators from the Lipschtiz Space to the Zygmund Space

In this paper, we give some estimates for the essential norm of weighted composition operators from the Lipschitz space to the Zygmund space.

Compact sums of Toeplitz products and Toeplitz algebra on the Dirichlet space

In this paper we consider Toeplitz operators on the Dirichlet space of the ball. We first characterize the compactness of operators which are finite sums of products of two Toeplitz operators. We also characterize Fredholm Toeplitz operators and describe the essential norm of Toeplitz operators. By using these results, we establish a short exact sequence associated with the $C^*$-algebra generated by all Toeplitz operators.