The Generalized Inverse of an Unbounded Linear Operator

1986 ◽  
Vol 17 (1) ◽  
pp. 128-131
Author(s):  
Robert Neff Bryan
Keyword(s):  
Linear Operator ◽  
Generalized Inverse ◽  
Unbounded Linear Operator

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].

scholarly journals The Quasi-Linear Operator Outer Generalized Inverse with Prescribed Range and Kernel in Banach Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Jianbing Cao ◽  
Yifeng Xue
Keyword(s):  
Linear Operator ◽  
Banach Spaces ◽  
Bounded Linear Operator ◽  
Generalized Inverse ◽  
Generalized Inverses ◽  
Bounded Linear ◽  
Perturbation Problems

Let and be Banach spaces, and let be a bounded linear operator. In this paper, we first define and characterize the quasi-linear operator (resp., out) generalized inverse (resp., ) for the operator , where and are homogeneous subsets. Then, we further investigate the perturbation problems of the generalized inverses and . The results obtained in this paper extend some well-known results for linear operator generalized inverses with prescribed range and kernel.

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 Chain-finite operators and locally chain-finite operators

2001 ◽  
Vol 43 (1) ◽  
pp. 113-121
Author(s):  
Teresa Bermúdez ◽  
Antonio Martinón
Keyword(s):  
Positive Integer ◽  
Linear Operator ◽  
Banach Spaces ◽  
Bounded Linear Operator ◽  
Generalized Inverse ◽  
Algebraic Characterization ◽  
Bounded Linear ◽  
A Chain

We give algebraic conditions characterizing chain-finite operators and locally chain-finite operators on Banach spaces. For instance, it is shown that T is a chain-finite operator if and only if some power of T is relatively regular and commutes with some generalized inverse; that is there are a bounded linear operator B and a positive integer k such that TkBTk =Tk and TkB=BTk. Moreover, we obtain an algebraic characterization of locally chain-finite operators similar to (1).

Sign in / Sign up

Export Citation Format

Share Document