We present ~2 resolution submillimeter observations of the submillimeter luminous giant Ly-alpha blob (LAB1) in the SSA 22 protocluster at redshift z=3.1 with the Submillimeter Array (SMA). Although the expected submillimeter flux density is 16 mJy at 880 micron, no emission is detected with the 2.4 x 1.9 (18 x 14 kpc) beam at the 3 sigma level of 4.2 mJy beam^{-1} in the SMA field of view of 35. This is in contrast to the previous lower angular resolution (15) observations where a bright (17 mJy) unresolved submillimeter source was detected at 850 micron toward the LAB1 using the Submillimeter Common-User Bolometer Array on the James Clerk Maxwell Telescope. The SMA non-detection suggests that the spatial extent of the submillimeter emission of LAB1 should be larger than 4 (>30 kpc). The most likely interpretation of the spatially extended submillimeter emission is that starbursts occur throughout the large area in LAB1. Some part of the submillimeter emission may come from spatially extended dust expelled from starburst regions by galactic superwind. The spatial extent of the submillimeter emission of LAB1 is similar to those of high redshift radio galaxies rather than submillimeter galaxies.
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