Linear operator algebra

Set

context $X$…left $\mathcal R$-module
definiendum $\langle \mathrm{Hom}(X,X),+,\cdot,*,\rangle \in L(X,X)$
context $\langle \mathrm{Hom}(X,X),+,\cdot\rangle \in \mathcal L(X,X)$
context $*:\mathrm{Hom}(X,X)\times \mathrm{Hom}(X,X)\to \mathrm{Hom}(X,X)$
$ v\in M $
$A,B \in \mathrm{Hom}(X,Y)$
postulate $(A*B)v = A(B v) $

Discussion

Theorem: A linear operator $A:X\to X$ is bijective if it has an inverse in $L(X,X)$.

Parents

Subset of

Unital associative algebra

Refinement of

Linear operator space