Numerical Range

Gustafson, Karl; Rao, Duggirala K. M.

doi:10.1007/978-1-4613-8498-4_1

Cited by 153 publications

(154 citation statements)

References 37 publications

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“…This is also the case for (unweighted) composition operators; see [1, page 846]. It is known that for a bounded operator T the numerical radius is at least ||T ||/2; see [12,. Therefore lower bounds for radii of discs discussed in Theorem 5.14 can be obtained using the norms of the operators.…”

Section: Corollary 52 Suppose Thatmentioning

confidence: 97%

Numerical ranges of weighted composition operators

Gunatillake

Jovovic

Smith

2014

Journal of Mathematical Analysis and Applications

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Abstract. The operator that takes the function f to ψf • φ is a weighted composition operator. We study numerical ranges of some classes of weighted composition operators on H 2 , the Hardy-Hilbert space of the unit disc. We consider the case where φ is a rotation of the unit disc and identify a class of convexoid operators. In the case of isometric weighted composition operators we give a complete classification of their numerical ranges. We also consider the inclusion of zero in the interior of the numerical range.

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Section: Corollary 52 Suppose Thatmentioning

confidence: 97%

Numerical ranges of weighted composition operators

Gunatillake

Jovovic

Smith

2014

Journal of Mathematical Analysis and Applications

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“…In particular, industrial organization networks provide a model class with sufficient fidelity to explore questions involving changes in market structure. The following lemma comes from various parts in [4].…”

Section: Stability Robustness Conditionsmentioning

confidence: 99%

“…Theorem 1: Consider an n-product market with agent set N = {1, 2, ..., n} and an industrial organization network characterized by (4). Let the Grand Coalition, G, of this network be given as in Definition 1, with objective function, U G , as specified in (2).…”

Section: Following the Same Reasoning Maxw (A +mentioning

confidence: 99%

Stability robustness conditions for market power analysis in industrial organization networks

Tran

Warnick

2008

2008 American Control Conference

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Abstract-Business networks provide one of the most compelling environments to study the conflicting effects of competition and cooperation on multi-agent dynamical systems. While firms engage various merger and divestiture strategies to create the desired cooperative environment that enhances their market power, governmental regulatory agencies enforce antitrust measures that protect competition as a means to limit the market power of these organizations. Merger simulation has subsequently evolved in recent years as a mechanism to study the impact of different organizational structures on the market. Nevertheless, typical economic models can often lead to competition dynamics that arbitrarily lose stability when considering different organizational structures. This work provides stability robustness conditions with respect to coalition structure for profit-maximizing dynamical systems with network demand, and partially convex utility. In particular, we show that stability of the coalition of all agents is sufficient to guarantee stability of all other coalition structures. These conditions are then leveraged to provide a systematic methodology for estimating a rich variety of demand systems that guarantee sensible stability results regardless of the structure of cooperation in the marketplace.

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“…The notion of the numerical range of an element in a normed algebra is well known and extensively studied during last five decades (see the standard references [2,3,5,6]). In this note we confine our self to unital C * -algebras.…”

Section: Introductionmentioning

confidence: 99%