Some properties of James type constant

Recently Takahashi has introduced James type constant. In this paper, we will introduce some new properties of the constant such as monotonicity, uniform non-squareness characterized by James type constant, and so on. We also investigate some relations between James type constant and other constants. Our main results of the paper are three examples of the constant. These examples include l p ( p ≥ 2 ) , l ∞ − l 1 , and X λ , p ( p ≥ 2 ) space, where X λ , p is the space l p with the norm | x | λ , p = max { ‖ x ‖ p , λ ‖ x ‖ ∞ } . We calculate exact values of James type constant in these concrete spaces.