• Title, Summary, Keyword: strong operator topology

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On the Iterated Duggal Transforms

  • Cho, Muneo;Jung, Il-Bong;Lee, Woo-Young
    • Kyungpook Mathematical Journal
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    • v.49 no.4
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    • pp.647-650
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    • 2009
  • For a bounded operator T = $U{\mid}T{\mid}$ (polar decomposition), we consider a transform b $\widehat{T}$ = ${\mid}T{\mid}U$ and discuss the convergence of iterated transform of $\widehat{T}$ under the strong operator topology. We prove that such iteration of quasiaffine hyponormal operator converges to a normal operator under the strong operator topology.

INTEGRAL OPERATORS FOR OPERATOR VALUED MEASURES

  • Park, Jae-Myung
    • Communications of the Korean Mathematical Society
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    • v.9 no.2
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    • pp.331-336
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    • 1994
  • Let $P_{0}$ be a $\delta$-ring (a ring closed with respect to the forming of countable intersections) of subsets of a nonempty set $\Omega$. Let X and Y be Banach spaces and L(X, Y) the Banach space of all bounded linear operators from X to Y. A set function m : $P_{0}$ longrightarrow L(X, Y) is called an operator valued measure countably additive in the strong operator topology if for every x $\epsilon$ X the set function E longrightarrow m(E)x is a countably additive vector measure. From now on, m will denote an operator valued measure countably additive in the strong operator topology.(omitted)

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q-FREQUENT HYPERCYCLICITY IN AN ALGEBRA OF OPERATORS

  • Heo, Jaeseong;Kim, Eunsang;Kim, Seong Wook
    • Bulletin of the Korean Mathematical Society
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    • v.54 no.2
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    • pp.443-454
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    • 2017
  • We study a notion of q-frequent hypercyclicity of linear maps between the Banach algebras consisting of operators on a separable infinite dimensional Banach space. We derive a sufficient condition for a linear map to be q-frequently hypercyclic in the strong operator topology. Some properties are investigated regarding q-frequently hypercyclic subspaces as shown in [5], [6] and [7]. Finally, we study q-frequent hypercyclicity of tensor products and direct sums of operators.

ON RELATIONSHIPS AMONG INTUITIONISTIC FUZZY APPROXIMATION OPERATORS, INTUITIONISTIC FUZZY TOPOLOGY AND INTUITIONISTIC FUZZY AUTOMATA

  • Tiwari, S.P.
    • Journal of applied mathematics & informatics
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    • v.28 no.1_2
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    • pp.99-107
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    • 2010
  • This paper is a study about the relationships among topologies and intuitionistic fuzzy topology induced, respectively, by approximation operators and an intuitionistic fuzzy approximation operator associated with an approximation space (X, R), when the relation R on X is precisely reflexive and transitive. In particular, we consider an intuitionistic fuzzy approximation operator on an approximation space X (i.e., a set X with a reflexive and transitive relation on it), which turns out to be an intuitionistic fuzzy closure operator. This intuitionistic fuzzy closure operator gives rise to two saturated fuzzy topologies on X and it turns out that all the level topologies of one of the fuzzy topology coincide and equal to the topology analogously induced on X by a crisp approximation operator. These observations are then applied to intuitionistic fuzzy automata.

𝓐-Frequent Hypercyclicity in an Algebra of Operators

  • Ahn, Ka Kyung
    • Journal of the Chosun Natural Science
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    • v.10 no.2
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    • pp.115-118
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    • 2017
  • We study a notion of $\mathcal{A}$-frequent hypercyclicity of linear maps between the Banach algebras consisting of operators on a separable infinite dimensional Banach space. We prove a sufficient condition for a linear map to satisfy the $\mathcal{A}$-frequent hypercyclicity in the strong operator topology.

A NOTE ON RADON-NIKODYM THEOREM FOR OPERATOR VALUED MEASURES AND ITS APPLICATIONS

  • Ahmed, Nasiruddin
    • Communications of the Korean Mathematical Society
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    • v.28 no.2
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    • pp.285-295
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    • 2013
  • In this note we present sufficient conditions for the existence of Radon-Nikodym derivatives (RND) of operator valued measures with respect to scalar measures. The RND is characterized by the Bochner integral in the strong operator topology of a strongly measurable operator valued function with respect to a nonnegative finite measure. Using this result we also obtain a characterization of compact sets in the space of operator valued measures. An extension of this result is also given using the theory of Pettis integral. These results have interesting applications in the study of evolution equations on Banach spaces driven by operator valued measures as structural controls.

FIXED POINTS OF BSC-SEQUENCES

  • Hosseini, Parviz Sadat;Yousefi, Bahmann
    • Communications of the Korean Mathematical Society
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    • v.32 no.4
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    • pp.899-908
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    • 2017
  • We call a sequence $(T_n)_n$ of bounded operators on a Banach space X, BSC-Sequence if it is a Cauchy sequence in the strong operator topology and is uniformly bounded below. We determine conditions under which such sequences has a fixed point.

Development of AC/DC Hybrid Simulation for Operator Training Simulator in Railway System

  • Cho, Yoon-Sung;Lee, Hansang;Jang, Gilsoo
    • Journal of Electrical Engineering and Technology
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    • v.9 no.1
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    • pp.52-59
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    • 2014
  • Operator training simulator, within a training environment designed to understand the principles and behavior of the railway system with respect to operator's entries and predefined scenario, can provide a very strong benefit in facilitating operators' handling undesired operations. This simulator consists of computer system and applications, and the purpose of applications is to generate the power and voltage and analyze the AC substation and DC railway, respectively. This paper describes a novel approach to the new techniques for AC/DC hybrid simulation for the operator training simulator in the railway system. We first propose the structure the database of railway system. Then, topology processing and power flow using a linked-list method based on the proposed database, full or decoupled newton-rapshon methods are presented. Finally, the interface between the analysis for AC substation using a newton-rapshon method and the analysis for DC railway system using a time-interval power flow method is described. We have verified and tested the developed algorithm through the extensive testing for the proposed test system. To demonstrate the validity of the developed algorithm, comparative simulations between the proposed algorithm and PSS/E for the test system were conducted.

BILBO Network: a proposal for communications in aircraft Structural Health Monitoring sensor networks

  • Monje, Pedro M.;Aranguren, Gerardo
    • Structural Monitoring and Maintenance
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    • v.1 no.3
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    • pp.293-308
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    • 2014
  • In the aeronautical environment, numerous regulatory and communication protocols exist that cover interconnection of on-board equipment inside the aircraft. Developed and implemented by the airlines since the 1960s, these communication systems are reliable, strong, certified and able to contact different sensors distributed throughout the aircraft. However, the scenario is slightly different in the structural health monitoring (SHM) field as the requirements and specifications that a global SHM communication system must fulfill are distinct. The number of SHM sensors installed in the aircraft rises into the thousands, and it is impossible to maintain all of the SHM sensors in operation simultaneously because the overall power consumption would be of thousands of Watts. This design of a new communication system must consider aspects as management of the electrical power supply, topology of the network for thousands of nodes, sampling frequency for SHM analysis, data rates, selected real-time considerations, and total cable weight. The goal of the research presented in this paper is to describe and present a possible integration scheme for the large number of SHM sensors installed on-board an aircraft with low power consumption. This paper presents a new communications system for SHM sensors known as the Bi-Instruction Link Bi-Operator (BILBO).