scholarly journals On an Unbounded Linear Operator Arising in the Theory of Growing Cell Population

1997 ◽  
Vol 211 (1) ◽  
pp. 273-294 ◽  
Author(s):  
Khalid Latrach ◽  
Mustapha Mokhtar-Kharroubi
Keyword(s):  
Linear Operator ◽  
Cell Population ◽  
Unbounded Linear Operator ◽  
Growing Cell

scholarly journals Dua Formula Eksponensial (Operator Linear dari Semigrup)

2021 ◽  
Vol 18 (1) ◽  
pp. 41-46
Author(s):  
L Meisaroh
Keyword(s):  
Linear Operator ◽  
Bounded Linear Operator ◽  
Infinitesimal Generator ◽  
The Other ◽  
Bounded Linear ◽  
Unbounded Linear Operator ◽  
C0 Semigroup

Assumed A is infinitesimal generator of C0-semigroup T(t) on X. This could be defined as T(t)=etA, applies if A is a bounded linear operator. Not if A is unbounded linear operator, then it will result in one possibility that show T(t) could be represented as etA. This paper will discuss and detail the proof of the other two formulas that show T(t) could be represented as etA.

scholarly journals Approximate Controllability of Semilinear Impulsive Evolution Equations

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Hugo Leiva
Keyword(s):  
Linear Operator ◽  
Evolution Equation ◽  
Hilbert Spaces ◽  
Approximate Controllability ◽  
Evolution Equations ◽  
Smooth Functions ◽  
Bounded Linear ◽  
Unbounded Linear Operator ◽  
Approximately Controllable ◽  
Impulsive Evolution Equations

We prove the approximate controllability of the following semilinear impulsive evolution equation:z'=Az+Bu(t)+F(t,z,u), z∈Z, t∈(0,τ], z(0)=z0, z(tk+)=z(tk-)+Ik(tk,z(tk),u(tk)), k=1,2,3,…,p,where0<t1<t2<t3<⋯<tp<τ,ZandUare Hilbert spaces,u∈L2(0,τ;U),B:U→Zis a bounded linear operator,Ik,F:[0,τ]×Z×U→Zare smooth functions, andA:D(A)⊂Z→Zis an unbounded linear operator inZwhich generates a strongly continuous semigroup{T(t)}t≥0⊂Z. We suppose thatFis bounded and the linear system is approximately controllable on[0,δ]for allδ∈(0,τ). Under these conditions, we prove the following statement: the semilinear impulsive evolution equation is approximately controllable on[0,τ].

Operator Estimates for Fredholm Modules

2000 ◽  
Vol 52 (4) ◽  
pp. 849-896 ◽  
Author(s):  
F. A. Sukochev
Keyword(s):  
Linear Operator ◽  
Symmetric Operator ◽  
Von Neumann Algebra ◽  
Operator Space ◽  
Von Neumann ◽  
Unbounded Linear Operator

AbstractWe study estimates of the typewhere φ(t) = t(1 + t2)−1/2, D0 = D0* is an unbounded linear operator affiliated with a semifinite von Neumann algebra , D − D0 is a bounded self-adjoint linear operator from and , where E(, τ) is a symmetric operator space associated with . In particular, we prove that φ(D) − φ(D0) belongs to the non-commutative Lp-space for some p ∈ (1,∞), provided belongs to the noncommutative weak Lr-space for some r ∈ [1, p). In the case and 1 ≤ p ≤ 2, we show that this result continues to hold under the weaker assumption . This may be regarded as an odd counterpart of A. Connes’ result for the case of even Fredholm modules.

scholarly journals Toeplitz Operators whose Symbols Are Borel Measures

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Jaehui Park
Keyword(s):  
Linear Operator ◽  
Toeplitz Operators ◽  
Borel Measure ◽  
Singular Measure ◽  
Borel Measures ◽  
Unbounded Linear Operator ◽  
Complex Borel Measure ◽  
Definition Of ◽  
Densely Defined ◽  
Complex Borel Measures

In this paper, we are concerned with Toeplitz operators whose symbols are complex Borel measures. When a complex Borel measure μ on the unit circle is given, we give a formal definition of a Toeplitz operator T μ with symbol μ , as an unbounded linear operator on the Hardy space. We then study various properties of T μ . Among them, there is a theorem that the domain of T μ is represented by a trichotomy. Also, it was shown that if the domain of T μ contains at least one polynomial, then T μ is densely defined. In addition, we give evidence for the conjecture that T μ with a singular measure μ reduces to a trivial linear operator.

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