What does $p+q \leq 1$ means in the context of $C^*$-algebra?

Question

Let $A$ be a $C^*$-algebra, and let $p,q \in A$. The book I'm following(An Introduction to K-theory for $C^*$-algebra) has this notation $p+q \leq 1$.

What does this mean? I looked through the book, but it seems like I have missed where they explained this notation.

Thank you.

Answer 1

In a C$^*$-algebra, $a\leq b$ means that $b-a$ is positive.

As a comment/advice, the book you are reading has this as its very first paragraph:

This chapter contains some basic facts about C*-algebras that the reader is assumed to be (or become) familiar with. There are very few proofs given in this chapter, and the reader is referred to other sources, for example Murphy's book [29], for details.

This book is written for someone already familiar with C$^*$-algebras, with a focus on K-theory. In my personal opinion, you should get some proficiency in C$^*$-algebras first.