Sentence examples for map of index from inspiring English sources

Let X, Y be real normed spaces and L : D ( L ) ⊂ X → Y a linear Fredholm map of index zero.

Then dim Ker ( L ) = dim Im ( Q ) = codim Im ( L ) = 4, L is a Fredholm map of index zero.

Since dim Ker L = dim Im Q = codim Im L = 2, thus L is a Fredholm map of index zero.

The parameters in the multi-point boundary conditions are such that the corresponding differential operator is a Fredholm map of index zero.

Let X, Z be real Banach spaces, L : dom ( L ) ⊂ X → Z be a Fredholm map of index zero and P X → X X, Q Z → Z Z be continuous projectors such that Im ( P ) = Ker ( L ), Ker ( Q ) = Im ( L ) and X = Ker ( L ) ⊕ Ker ( P ), Z = Im ( L ) ⊕ Im ( Q ).

Let Y, Z be real Banach spaces, (L:operatorname{dom} L subset Y to Z) be a Fredholm map of index zero and (P Yto Y), (Q:Zto Z) be continuous projectors such that operatorname{Ker} L =operatorname{Im}P,qquad operatorname{Im}L= operatorname{Ker} Q,qquad Y=operatorname{Ker} L oplusoperatorname{ Ker P, qquad Z=operatorname{Im}L oPlusoperatorname{Im}qquad

Let L be a Fredholm mapping of index zero.

Therefore, L is a Fredholm mapping of index zero.

Therefore, is a Fredholm mapping of index zero.

This means L is a Fredholm mapping of index zero.

L Dom L ⊂ X X → Y is a Fredholm mapping of index zero.