Prefixing schema name

Hi,
Would it be possible to create a table or index in a schema without
prefixing the schema name? I find it a hassle to keep specifying the schema
name when I create an object or performing DMLs in a schema. The
search_path configuration works only for queries.

For example:
Is there a way to run the create/insert statements below without prefixing
the schema name, user1?

As the user, user1:
Create table user1.table1 (id int);
Insert into user1.table1 values (1);

Thanks.