Modulus and characteristic of convexity: Difference between revisions

Revision as of 18:39, 5 July 2021

Revision as of 16:25, 23 August 2021

Line 17:

| first = Mahlon

| title = Uniform convexity in factor and conjugate spaces

| journal = Ann.Annals of Math.Mathematics |series = 2

| volume = 45

| year = 1944

Line 34:

* When ''X'' is uniformly convex, it admits an equivalent norm with power type modulus of convexity.<ref>see {{citation

| last=Pisier |first=Gilles |author-link=Gilles Pisier

| title= Martingales with values in uniformly convex spaces | journal=[[Israel J.Journal Math.of Mathematics]] | volume=20 | year=1975 | issue=3–4 | pages=326–350 | doi = 10.1007/BF02760337 | doi-access=free | mr=394135|s2cid=120947324 }}

.</ref> Namely, there exists {{nowrap|''q'' &ge; 2}} and a constant&nbsp;{{nowrap|''c'' &gt; 0}} such that

::<math>\delta(\varepsilon) \ge c \, \varepsilon^q, \quad \varepsilon \in [0, 2].</math>

Line 75:

| first = James

| title = Uniformly convex spaces

| journal = Trans.Transactions Amer.of Math.the Soc.American Mathematical Society

| volume = 40

| year = 1936