I read the book "K-theory for operator algebras" and I have a question about the definition of Kasparov modules for graded $C^*$-algebras $A$ and $B$.
Definition: Let $A$ and $B$ graded $C^*$-algebras. A Kasparov $A-B$-module is a triple $\epsilon=(E,\phi , T)$, where $E$ is a countably graded Hilbert$-B$-module, $\phi:A\to B(E)$ is a graded $\ast$-homomorphism and $T$ is a degree 1 operator, such that $[\phi(a),T],\; \phi(a)(T^2-id_E),\; \phi (a)(T-T^*)$ are all in $K(E)$ for all $a\in A$.
My question is: what is a degree 1 operator in this context? The grading on $E$ induces a grading $B(E)$, and $T$ is an element of the summand $B(E)^{(1)}$ of the grading, if I understand it correctly. But how does the grading on $B(E)$ look like? What does $T\in B(E)^{(1)}$ mean?