I'm struggling to understand the motivation for the $\gamma$-operations in the context of $\lambda$-rings, with specific application to topological $K$-theory.
Given a $\lambda$-ring, $R$, the $\lambda$-operations have the property that $\lambda_t(x)$ is a polynomial of order $dim(x)$. The augmentation ideal $I$ does not contain many finite dimensional elements, so we define the $\gamma$-operations which have the property that $\gamma_t(x)$ is polynomial on $I$.
There then seem to be two main results to follow from this:
1) We prove that the operations on $\gamma$-rings are $\mathbb{Z}[\gamma_1, \dots]^+$, or that $Op(K_1, K) = \mathbb{Z}[[\gamma_1, \dots]]$.
2) We can discuss the $\gamma$-filtration and it's properties.
I don't fully understand the need for the $\gamma$-operations, they are just a linear combination of the $\lambda$-operations. Why do we choose to work with them? Moreover, why can we not talk about a $\lambda$-filtration defined in similar way and work with this instead?
My references I've been working from are Atiyah's $K$-theory and Yau's Lambda-rings.
Thanks for any help!